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NOTE
Created on 2024-02-07T20:54:31.1029159Z by ClassTranscribe

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All right.

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Good morning, everybody.

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Hope you had a good weekend.

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Form relatively.

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Alright, so I'm going to get started.

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So in the previous lectures we've

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mainly learned about how to build and

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apply single models.

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So we talked about nearest neighbor,

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logistic regression, linear regression,

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and trees.

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And so now we're going to.

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Talk about how to build collection of

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models and use them for prediction.

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So that technique is called ensembles

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and ensemble is when you build a bunch

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of models and then you average their

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predictions or you train them in a way

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that they build on top of each other.

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So some of you might remember this show

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who wants to be a millionaire?

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The idea of this show is that there's a

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contestant and they get asked a series

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of questions and they have multiple

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choice answers and if they get it right

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then like the dollar value that they

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would bring home increases, but if they

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ever get it wrong, then they go home

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with nothing.

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And they had three forms of help.

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One of the forms was that they could

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eliminate 2 of the incorrect choices.

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Another form is that they could call a

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friend.

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So they would have like people.

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They would have friends at home that

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they think have like various expertise.

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And if they see a question that they

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think is really hard and they're not

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sure of the answer, they could choose

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which friend to call to give them the

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answer.

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The third, the third form of help they

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could get is pull the audience so.

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They would ask the audience to vote on

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the correct answer.

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And the audience would all vote, and

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then they could make a decision based

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on that.

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And they could use each of these forms

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of help one time.

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What do you which of these do you think

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between pull the audience and call a

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friend?

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Which of these do you think is a is

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more likely to give the correct answer?

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Alright, so how many people think it's

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pulled the audience?

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How many people think it's for in a

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friend?

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So the audience is correct, it's pulled

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the audience.

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But they did statistics.

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They looked at analysis of the show and

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on average the audience is correct 92%

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of the time.

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And call a friend is correct 66% of the

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time.

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So that might be kind of unintuitive,

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especially the margin, because.

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When you get to call a friend, you get

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to call somebody who you think knows

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about the particular subject matter.

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So they're an expert.

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You would expect that out of.

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You would expect that they would be

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much, much more informed than an

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average audience member who is just

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there to be entertained.

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But the audience is actually much more

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accurate and that kind of that

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demonstrates the power of ensembles

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that averaging multiple weak

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predictions.

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Is often more accurate than any single

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predictor, even if that single

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predictor is pretty good.

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It's possible to construct models to

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construct ensembles in different ways.

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One of the ways is that you

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independently train a bunch of

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different models by resampling the data

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or resampling features, and then you

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average those the predictions of those

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models.

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Another is that you incrementally train

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new models that try to fix the mistakes

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of the previous models.

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So we're going to talk about both of

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those.

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And they work on different principles.

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There's different reasons why each one

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is a is a reasonable choice.

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So the theory behind ensembles really

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comes down to this theorem called the

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balance, the bias variance tradeoff.

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And this is a really fundamental

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concept in machine learning.

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And I'm not going to go through the

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derivation of it, it's at this link

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here.

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It's not.

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It's not really, it's something that

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anyone could follow along, but it does

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take a while to get through it.

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But it's a really fundamental idea in

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machine learning.

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So in terms of one way that you can

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express it is in terms of the squared

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error of prediction.

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So for regression, but there's also

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equivalent theorems for classification,

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for 01 classification or for log

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probability loss.

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And it all works out to the same thing,

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which is that you're expected test

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error.

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So what this means is that.

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If you were to randomly choose some

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number of samples from the general

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distribution of data.

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Then the expected error that you would

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get for the model that you've trained

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on your sample of data compared to what

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it should have predicted.

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Has three different components, so one

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component is the variance.

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The variance is that if UV sampled that

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same amount of data multiple times from

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the general distribution, you'd get

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different data samples and that would

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lead to different models that make

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different predictions on the same test

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data.

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So you have some variance in your

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prediction.

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That's due to the randomness of

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sampling your model.

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Or it could be due to if you have a

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randomized optimization.

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It could also be due to the

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randomization of the optimization.

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So this is a variance mainly due to

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resampling data of your model.

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Compared to your expected model.

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So this is how the sum of the average

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square distance between the predictions

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of an individual model and the average

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over all possible models that you would

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learn from sampling the data many

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times.

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Then there's a skip over here for now.

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Then there's a bias component squared.

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So the bias is if you were to sample

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the data infinite times, train your

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infinite models and average them, then

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you get this expected prediction.

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So it's the expected the average

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prediction of all of those infinite

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models that you trained with the same

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amount of data.

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And if you look at the difference

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between that and the true prediction,

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then that's your bias.

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So if you have no bias, then obviously

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if you have no bias this would be 0.

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If on average your models would

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converge to the true answer, this will

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be 0.

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But if your models tend to predict too

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high or too low on average, then this

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will be nonzero.

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And then finally there's the noise.

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So this is kind of like the irreducible

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error due to the problem that it might

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be that for the exact same input

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there's different outputs that are

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possible, like if you're trying to

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predict temperature or read characters

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or something like that, the features

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are not sufficient to completely

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identify the correct answer.

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So there's these three parts to the

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error.

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There's the variance due to limited

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data in your models due to the

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randomness in a model.

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That's either due to randomly sampling

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the data or due to your optimization.

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There's the bias, which is due to the

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inability of your model to fit the true

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solution.

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And there's a noise which is due to the

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problem characteristics or the

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inability to make a perfect prediction

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from the features.

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Yeah.

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So here, so why is a particular?

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That particular label assigned to X&Y

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bar is the average of all the labels

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that you would that could be assigned

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to ex.

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So for example, if you had imagine that

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you had the exact same, let's say your

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prediction predicting temperature based

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on the last five days.

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And you saw that exact same scenario of

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the last five days like 15 times, but

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you had different next day

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temperatures.

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So why would be like one of those next

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day temperatures and why bar is the

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average of those next day temperatures?

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Question.

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How is your model?

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So HD is a model that's trained on a

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sample on a DF sample of the

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distribution.

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And H bar is the average of all such

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models.

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So the bias and variance is illustrated

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here.

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So imagine that you're trying to shoot

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a target.

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Then if you have low bias and low

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variance, it means that all your shots

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are clustered in the center of the

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target.

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If you have low bias and high variance

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means that the average of your shots is

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in the center of your target, but the

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shots are more widely distributed.

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If you have high bias and low variance,

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it means that your shots are clustered

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tight together, but they're off the

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center.

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And if you have high bias and high

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variance, then both they're dispersed,

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dispersed, and they're off the center.

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So you can see from even from this

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illustration that obviously low bias

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and low variance is the best, but both

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variance and bias caused some error,

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and high bias and high variance has the

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greatest average error.

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You also often see a expressed in a

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plot like this, where you're looking at

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your model complexity and this is like.

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This is kind of like a classic

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overfitting plot, so this model

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complexity could for example be the

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height of your tree.

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So if you train a tree with two leaf

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nodes with just a height of 1, then

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you're going to have a very low

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variance.

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If you were to resample the data many

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times and train that short tree, you

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would very likely get a very similar

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tree every single time, so the variance

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is low.

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That's the blue curve.

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But the bias is high.

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You're unlikely to make very good

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predictions with that really short

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tree.

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Even if you averaged an infinite number

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of them, you would still.

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You would still have a lot of error.

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As you increase the depth of the tree,

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your bias drops.

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You're able to make better predictions

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on your on average.

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But the variance starts to increase.

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The trees start to look more different

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from each other.

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So if you train a full tree so that

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there's one data point per leaf node,

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then the trees are going to look pretty

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different when you resample the data

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because you'll have different data

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samples.

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So eventually, at some point you reach

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some ideal situation where the bias

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plus the bias squared plus the variance

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is minimized, and that's when you'd

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want to, like, stop if you're trying to

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choose hyperparameters.

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And if you train more complex models,

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it's going to continue to reduce the

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bias, but the increase in variance is

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going to cause your test error to

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increase.

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So if you're thinking about it in terms

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of a single model, really this, then

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you would be thinking about it in terms

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of the plot that I just showed where

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you're trying to figure out like what

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complexity, if it's a model that can

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have varying complexity trees or neural

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networks, like how complex should my

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model be in order to best.

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Find the balance between the bias and

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the variance.

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But ensembles have a different way to

00:13:05.910 --> 00:13:08.050
directly combat the bias and the

00:13:08.050 --> 00:13:10.430
variance, so I'm going to talk about a

00:13:10.430 --> 00:13:12.470
few ensemble methods and how they

00:13:12.470 --> 00:13:12.920
relate.

00:13:16.400 --> 00:13:19.130
The first one is called first, like.

00:13:19.130 --> 00:13:20.580
This is actually not one of these

00:13:20.580 --> 00:13:22.007
ensemble method, but it is an ensemble

00:13:22.007 --> 00:13:22.245
method.

00:13:22.245 --> 00:13:23.690
It's the simplest of these, and it's

00:13:23.690 --> 00:13:25.219
kind of the foundation of the ensemble

00:13:25.220 --> 00:13:25.810
methods.

00:13:25.810 --> 00:13:28.010
So it's a statistical technique called

00:13:28.010 --> 00:13:28.710
bootstrapping.

00:13:29.860 --> 00:13:32.740
Imagine that, for example, I wanted to

00:13:32.740 --> 00:13:35.170
know what is the average age of

00:13:35.170 --> 00:13:36.380
somebody in this class.

00:13:37.610 --> 00:13:39.990
One way that I could do it is I could

00:13:39.990 --> 00:13:42.323
ask each of you your ages and then I

00:13:42.323 --> 00:13:43.840
could average it, and then that might

00:13:43.840 --> 00:13:45.605
give me like an estimate for the

00:13:45.605 --> 00:13:47.110
average age of all the students in the

00:13:47.110 --> 00:13:47.450
class.

00:13:48.720 --> 00:13:51.700
But maybe I not only want to know the

00:13:51.700 --> 00:13:53.850
average age, but I also want some

00:13:53.850 --> 00:13:56.020
confidence range on that average age.

00:13:56.020 --> 00:13:58.210
And if all I do is I average all your

00:13:58.210 --> 00:14:00.960
ages, that doesn't tell me how likely I

00:14:00.960 --> 00:14:02.930
am to be within, say, like three years.

00:14:04.000 --> 00:14:07.090
And so one way, one way that I can

00:14:07.090 --> 00:14:09.950
solve that problem is with bootstrap

00:14:09.950 --> 00:14:13.590
estimation where I resample the data

00:14:13.590 --> 00:14:15.530
multiple times so I could choose.

00:14:15.530 --> 00:14:18.800
I could take 50 samples and sample with

00:14:18.800 --> 00:14:21.235
repetition so I could potentially call

00:14:21.235 --> 00:14:22.350
the same person twice.

00:14:23.160 --> 00:14:24.125
Ask your ages.

00:14:24.125 --> 00:14:26.750
Ask the ages of 50 individuals.

00:14:26.750 --> 00:14:28.140
Again, the same individual may be

00:14:28.140 --> 00:14:28.870
repeated.

00:14:28.870 --> 00:14:31.530
I take the average from that and repeat

00:14:31.530 --> 00:14:33.810
that many times, and then I can look at

00:14:33.810 --> 00:14:35.579
the variance of those estimates that I

00:14:35.580 --> 00:14:35.800
get.

00:14:36.470 --> 00:14:38.050
And then I can use the variance of

00:14:38.050 --> 00:14:40.430
those estimates to get a confidence

00:14:40.430 --> 00:14:42.570
range on my estimate of the mean.

00:14:43.810 --> 00:14:47.080
So bootstrap bootstrapping is a way to.

00:14:47.190 --> 00:14:50.710
To estimate a particular parameter, in

00:14:50.710 --> 00:14:53.035
this case the average age, as well as

00:14:53.035 --> 00:14:55.040
my variance of my estimate of that

00:14:55.040 --> 00:14:55.690
parameter.

00:14:55.690 --> 00:14:58.550
So like how far off am I would expect

00:14:58.550 --> 00:14:58.970
to be?

00:15:02.560 --> 00:15:04.300
We can apply that idea to

00:15:04.300 --> 00:15:08.918
classification to try to produce a more

00:15:08.918 --> 00:15:11.266
stable estimate of the mean or to

00:15:11.266 --> 00:15:13.370
produce a more stable prediction.

00:15:13.370 --> 00:15:15.270
In other words, to reduce the variance

00:15:15.270 --> 00:15:17.930
of my classifiers given a particular

00:15:17.930 --> 00:15:18.620
data sample.

00:15:20.250 --> 00:15:23.010
So the method is called bagging, which

00:15:23.010 --> 00:15:24.890
stands for aggregate bootstrapping.

00:15:25.990 --> 00:15:27.390
And the idea is pretty simple.

00:15:28.630 --> 00:15:32.340
For M different times capital M, So I'm

00:15:32.340 --> 00:15:34.730
going to train train M classifiers.

00:15:35.430 --> 00:15:37.620
I draw some number of samples which

00:15:37.620 --> 00:15:39.533
should be less than my total number of

00:15:39.533 --> 00:15:40.800
samples, but I'm going to draw them

00:15:40.800 --> 00:15:41.828
with replacement.

00:15:41.828 --> 00:15:43.860
Draw with replacement means I can

00:15:43.860 --> 00:15:45.310
choose the same sample twice.

00:15:46.750 --> 00:15:48.410
Then I train a classifier on those

00:15:48.410 --> 00:15:51.120
samples, and then at the end my final

00:15:51.120 --> 00:15:54.290
classifier is an average of all of my

00:15:54.290 --> 00:15:55.620
predictions from the individual

00:15:55.620 --> 00:15:56.340
classifiers.

00:15:57.080 --> 00:15:59.040
So if I'm doing regression, I would

00:15:59.040 --> 00:16:01.940
just be averaging the continuous values

00:16:01.940 --> 00:16:04.200
that the classifiers are aggressors

00:16:04.200 --> 00:16:04.890
predicted.

00:16:04.890 --> 00:16:07.555
If I'm doing classification, I would

00:16:07.555 --> 00:16:10.116
average the probabilities or average

00:16:10.116 --> 00:16:13.056
the most likely label from each of the

00:16:13.056 --> 00:16:13.389
classifiers.

00:16:14.380 --> 00:16:16.810
And there's lots of theory that shows

00:16:16.810 --> 00:16:19.100
that this increases the stability of

00:16:19.100 --> 00:16:21.500
the classifier and reduces reduces the

00:16:21.500 --> 00:16:24.915
variance, and so the average of a bunch

00:16:24.915 --> 00:16:26.630
of classifiers trained this way.

00:16:27.300 --> 00:16:30.110
Typically outperform any individual

00:16:30.110 --> 00:16:30.840
classifier.

00:16:32.030 --> 00:16:33.870
In these classifiers will be different

00:16:33.870 --> 00:16:36.490
from each other because there's a

00:16:36.490 --> 00:16:37.100
difference.

00:16:37.100 --> 00:16:39.670
Because the data is, a different sample

00:16:39.670 --> 00:16:41.030
of data is drawn to train each

00:16:41.030 --> 00:16:41.590
classifier.

00:16:45.070 --> 00:16:46.790
So that's the question.

00:17:00.050 --> 00:17:02.463
So not yeah, but not features, it's

00:17:02.463 --> 00:17:03.186
samples.

00:17:03.186 --> 00:17:06.700
So I have say 1000 data samples.

00:17:07.340 --> 00:17:10.770
And I draw say 900 data samples, but

00:17:10.770 --> 00:17:13.467
they're not 900 out of the thousand,

00:17:13.467 --> 00:17:16.190
it's 900 with repetition.

00:17:16.190 --> 00:17:17.720
So there might be 1 sample that I

00:17:17.720 --> 00:17:19.596
choose draw three times, others that I

00:17:19.596 --> 00:17:21.259
draw no times, others that I draw one

00:17:21.260 --> 00:17:21.850
time.

00:17:21.850 --> 00:17:23.700
So you can in terms of like

00:17:23.700 --> 00:17:26.840
programming, you would just do a random

00:17:26.840 --> 00:17:31.290
like 0 to 1 * N and then and then turn

00:17:31.290 --> 00:17:33.397
it into an integer and then you get

00:17:33.397 --> 00:17:35.159
like you get a random sample with

00:17:35.160 --> 00:17:35.660
replacement.

00:17:46.940 --> 00:17:47.720
Typically.

00:17:47.720 --> 00:17:49.626
So usually each of the classifiers is

00:17:49.626 --> 00:17:50.820
of the same form.

00:17:50.820 --> 00:17:51.190
Yep.

00:17:53.550 --> 00:17:55.270
So this is the idea behind random

00:17:55.270 --> 00:17:57.760
forests, which is a really powerful

00:17:57.760 --> 00:17:59.940
classifier, but very easy to explain at

00:17:59.940 --> 00:18:01.500
least once you once you know about

00:18:01.500 --> 00:18:02.270
decision trees.

00:18:03.780 --> 00:18:06.040
So in a random forest, train a

00:18:06.040 --> 00:18:07.150
collection of trees.

00:18:08.140 --> 00:18:09.970
For each tree that you're going to

00:18:09.970 --> 00:18:11.786
train, you sample some fraction in the

00:18:11.786 --> 00:18:13.880
data, for example 90% of the data.

00:18:13.880 --> 00:18:15.620
Sometimes people just sample all the

00:18:15.620 --> 00:18:15.990
data.

00:18:16.430 --> 00:18:19.948
Then you randomly sample some number of

00:18:19.948 --> 00:18:20.325
features.

00:18:20.325 --> 00:18:23.042
So for regression, one suggestion is to

00:18:23.042 --> 00:18:24.648
use 1/3 of the features.

00:18:24.648 --> 00:18:28.003
For classification you would use like.

00:18:28.003 --> 00:18:30.000
Some suggestions are to use like a

00:18:30.000 --> 00:18:31.565
square root of the number of features.

00:18:31.565 --> 00:18:32.240
So if there's.

00:18:32.970 --> 00:18:36.260
If there are 400 features, then you

00:18:36.260 --> 00:18:38.290
randomly sample 20 of them.

00:18:38.290 --> 00:18:40.240
Or another suggestion is to use log

00:18:40.240 --> 00:18:40.820
base 2.

00:18:41.650 --> 00:18:43.389
It's not really that critical, but you

00:18:43.389 --> 00:18:44.820
want you want the number of features

00:18:44.820 --> 00:18:46.995
that you select to be much less than

00:18:46.995 --> 00:18:48.430
the total number of features.

00:18:49.110 --> 00:18:51.800
So here previously I was talking about

00:18:51.800 --> 00:18:53.760
when I say sample the data, what I mean

00:18:53.760 --> 00:18:55.870
is like is choosing a subset of

00:18:55.870 --> 00:18:56.790
training samples.

00:18:57.910 --> 00:19:00.290
But when I say sample the features, I

00:19:00.290 --> 00:19:02.699
mean choose a subset of the features of

00:19:02.699 --> 00:19:05.365
the columns of your of your matrix if

00:19:05.365 --> 00:19:06.914
the rows are samples and the columns

00:19:06.914 --> 00:19:07.350
are features.

00:19:09.360 --> 00:19:11.710
So the you need to sample the features

00:19:11.710 --> 00:19:13.210
because otherwise if you train the tree

00:19:13.210 --> 00:19:14.693
you're going to get the same result if

00:19:14.693 --> 00:19:17.720
you're doing like minimizing the

00:19:17.720 --> 00:19:19.440
maximizing mutual information for

00:19:19.440 --> 00:19:19.890
example.

00:19:20.700 --> 00:19:22.270
If you were to sample all your data and

00:19:22.270 --> 00:19:23.600
all the features, you would just train

00:19:23.600 --> 00:19:24.280
the same tree.

00:19:25.070 --> 00:19:27.660
MN times and that would give you no

00:19:27.660 --> 00:19:28.160
benefit.

00:19:28.900 --> 00:19:30.240
All right, so you randomly sample some

00:19:30.240 --> 00:19:31.540
features, train a tree.

00:19:32.240 --> 00:19:34.497
Optionally, you can estimate your

00:19:34.497 --> 00:19:36.020
validation error on the data that

00:19:36.020 --> 00:19:38.283
wasn't used to train that tree, and you

00:19:38.283 --> 00:19:41.140
can use the average of those validation

00:19:41.140 --> 00:19:44.513
errors in order to get a estimate of

00:19:44.513 --> 00:19:46.930
your error for the for your final

00:19:46.930 --> 00:19:47.480
collection.

00:19:50.000 --> 00:19:51.886
And after you've trained all the trees,

00:19:51.886 --> 00:19:54.610
you just do that 100 times or whatever.

00:19:54.610 --> 00:19:55.920
It's completely independent.

00:19:55.920 --> 00:19:58.330
So it's just like a very if you've got

00:19:58.330 --> 00:19:59.920
code to train a tree, it's just a very

00:19:59.920 --> 00:20:01.090
small loop.

00:20:02.370 --> 00:20:04.990
And then at the end you average the

00:20:04.990 --> 00:20:06.766
prediction of all the trees.

00:20:06.766 --> 00:20:08.930
So usually you would train your trees

00:20:08.930 --> 00:20:09.535
to completion.

00:20:09.535 --> 00:20:12.160
So if you're doing like classification

00:20:12.160 --> 00:20:14.850
or in either case you would end up with

00:20:14.850 --> 00:20:16.480
a leaf node that contains one data

00:20:16.480 --> 00:20:16.926
sample.

00:20:16.926 --> 00:20:19.060
So you're training like very high

00:20:19.060 --> 00:20:21.530
variance trees, they're deep trees.

00:20:22.650 --> 00:20:24.760
That have low bias, they can fit the

00:20:24.760 --> 00:20:27.580
training data perfectly, but.

00:20:29.470 --> 00:20:31.027
But then you're going to average all of

00:20:31.027 --> 00:20:31.235
them.

00:20:31.235 --> 00:20:34.534
So you start out with high bias or high

00:20:34.534 --> 00:20:36.650
variance, low bias classifiers, and

00:20:36.650 --> 00:20:37.743
then you average them.

00:20:37.743 --> 00:20:40.044
So you end up with low bias, low

00:20:40.044 --> 00:20:40.669
variance classifiers.

00:20:49.930 --> 00:20:51.310
Yes, for each tree.

00:20:51.310 --> 00:20:52.460
Yeah, for each tree.

00:20:52.630 --> 00:20:53.160
Yeah.

00:20:59.180 --> 00:21:02.920
You increase the number of trees, yeah,

00:21:02.920 --> 00:21:03.410
so.

00:21:04.110 --> 00:21:07.720
If you if so, think of it this way.

00:21:07.720 --> 00:21:12.075
If I were to if I were to try to

00:21:12.075 --> 00:21:14.995
estimate the sum of your ages, then as

00:21:14.995 --> 00:21:17.900
I ask you your ages and add them up, my

00:21:17.900 --> 00:21:19.463
estimate of the variance of the

00:21:19.463 --> 00:21:21.288
variance on the estimate, the sum is

00:21:21.288 --> 00:21:23.400
going to increase linearly, right?

00:21:23.400 --> 00:21:26.680
It's going to keep on increasing until

00:21:26.680 --> 00:21:30.660
sum is 100,000 ± 10,000 or something.

00:21:31.480 --> 00:21:33.168
But if I'm trying to estimate the

00:21:33.168 --> 00:21:35.700
average of your ages and I keep on

00:21:35.700 --> 00:21:38.250
asking your ages, then my variance is

00:21:38.250 --> 00:21:39.950
going to go down South.

00:21:39.950 --> 00:21:43.040
The variance of the sum is North Times

00:21:43.040 --> 00:21:47.030
Sigma squared, but the variance of the

00:21:47.030 --> 00:21:50.980
average is N over Sigma I think just no

00:21:50.980 --> 00:21:53.688
over Sigma or sorry, Sigma over N,

00:21:53.688 --> 00:21:56.100
Sigma squared over N the variance of

00:21:56.100 --> 00:21:58.513
the average is Sigma squared over N,

00:21:58.513 --> 00:22:01.269
but the variance of the sum is N.

00:22:01.330 --> 00:22:02.500
Times Sigma squared.

00:22:04.490 --> 00:22:06.934
So the average reduces the variance.

00:22:06.934 --> 00:22:08.135
Yeah, so if I.

00:22:08.135 --> 00:22:09.960
So by averaging the trees I reduce the

00:22:09.960 --> 00:22:10.160
variance.

00:22:14.870 --> 00:22:17.250
So that's random forests and I will

00:22:17.250 --> 00:22:17.840
talk more.

00:22:17.840 --> 00:22:20.467
I'll give an example of use of random

00:22:20.467 --> 00:22:22.280
forests and I'll talk about like some

00:22:22.280 --> 00:22:24.780
studies about the performance of

00:22:24.780 --> 00:22:26.750
various classifiers including random

00:22:26.750 --> 00:22:27.320
forests.

00:22:27.320 --> 00:22:29.946
But before I do that, I want to talk

00:22:29.946 --> 00:22:31.330
about boosting, which is the other

00:22:31.330 --> 00:22:31.890
strategy.

00:22:33.860 --> 00:22:36.080
So I have the boosting terms here as

00:22:36.080 --> 00:22:36.490
well.

00:22:37.730 --> 00:22:38.170
All right.

00:22:38.170 --> 00:22:41.085
So the first version of boosting and

00:22:41.085 --> 00:22:42.740
one other thing I want to say about

00:22:42.740 --> 00:22:45.350
this is random forest was popularized

00:22:45.350 --> 00:22:47.885
by this paper by Bremen in 2001.

00:22:47.885 --> 00:22:50.460
So decision trees go back to the 90s at

00:22:50.460 --> 00:22:53.893
least, but they were never really, like

00:22:53.893 --> 00:22:56.680
I said, were they're good for helping

00:22:56.680 --> 00:22:59.750
for making decisions that people can

00:22:59.750 --> 00:23:01.360
understand, that you can communicate

00:23:01.360 --> 00:23:02.780
and explain like why it made this

00:23:02.780 --> 00:23:03.130
decision.

00:23:03.890 --> 00:23:05.710
And they're good for analyzing data,

00:23:05.710 --> 00:23:07.040
but they're not really very good

00:23:07.040 --> 00:23:08.770
classifiers or aggressors compared to

00:23:08.770 --> 00:23:09.880
other methods that are out there.

00:23:11.210 --> 00:23:14.390
But Bremen popularized random forests

00:23:14.390 --> 00:23:16.530
in 2001 and showed that the

00:23:16.530 --> 00:23:19.050
combinations of trees is actually super

00:23:19.050 --> 00:23:20.380
powerful and super useful.

00:23:21.840 --> 00:23:23.770
And provides like the theory for why it

00:23:23.770 --> 00:23:25.800
works and why you should be sampling

00:23:25.800 --> 00:23:27.780
different subsets of features, and the

00:23:27.780 --> 00:23:29.160
idea that you want the trees to be

00:23:29.160 --> 00:23:30.000
decorrelated.

00:23:31.000 --> 00:23:34.130
To make different predictions but also

00:23:34.130 --> 00:23:34.800
be powerful.

00:23:37.140 --> 00:23:37.710
Alright.

00:23:37.710 --> 00:23:41.140
So the other strategy is boosting and

00:23:41.140 --> 00:23:42.910
the first boosting paper I think was

00:23:42.910 --> 00:23:44.630
Shapira in 1989.

00:23:45.500 --> 00:23:46.900
And that's one was pretty simple.

00:23:47.680 --> 00:23:51.090
So the idea was that you first randomly

00:23:51.090 --> 00:23:52.690
choose a set of samples.

00:23:53.470 --> 00:23:55.280
Without replacement at this time.

00:23:55.280 --> 00:23:57.970
So if you've got 1000, you randomly

00:23:57.970 --> 00:24:00.133
choose, say, 800 of them without

00:24:00.133 --> 00:24:00.539
replacement.

00:24:01.440 --> 00:24:04.320
And you train a classifier on those

00:24:04.320 --> 00:24:07.140
samples, that's the weak learner, C1.

00:24:07.760 --> 00:24:10.170
So I've got the notation over here in

00:24:10.170 --> 00:24:12.060
the literature you'll see things like

00:24:12.060 --> 00:24:15.140
learner, hypothesis, classifier, they

00:24:15.140 --> 00:24:16.130
all mean the same thing.

00:24:16.130 --> 00:24:17.560
There's something that's some model

00:24:17.560 --> 00:24:18.810
that's doing some prediction.

00:24:19.960 --> 00:24:22.530
A weak learner is just a classifier

00:24:22.530 --> 00:24:25.260
that can achieve less than 50% training

00:24:25.260 --> 00:24:27.140
error over any training distribution.

00:24:27.910 --> 00:24:30.120
So almost any classifier we would

00:24:30.120 --> 00:24:32.217
consider is a weak learner.

00:24:32.217 --> 00:24:34.000
As long as you can guarantee that it

00:24:34.000 --> 00:24:35.970
will be able to get at least chance

00:24:35.970 --> 00:24:38.030
performance in a two class problem,

00:24:38.030 --> 00:24:39.309
then it's a weak learner.

00:24:42.560 --> 00:24:45.286
A strong learner is a combination of

00:24:45.286 --> 00:24:46.182
the weak learner.

00:24:46.182 --> 00:24:47.852
It's a predictor that uses a

00:24:47.852 --> 00:24:49.230
combination of the weak learners.

00:24:49.230 --> 00:24:52.020
So first you train 1 classifier in a

00:24:52.020 --> 00:24:52.940
subset of the data.

00:24:53.620 --> 00:24:55.936
Then you draw a new sample, and this

00:24:55.936 --> 00:24:58.490
new sample is drawn so that half the

00:24:58.490 --> 00:24:59.310
samples.

00:25:00.010 --> 00:25:04.960
Are misclassified by the 1st classifier

00:25:04.960 --> 00:25:06.640
and this can be drawn with replacement.

00:25:07.460 --> 00:25:10.172
So half of your N2 samples were

00:25:10.172 --> 00:25:12.310
misclassified by C1 and half of them

00:25:12.310 --> 00:25:14.009
were not misclassified by C1.

00:25:14.900 --> 00:25:17.230
And so now in this new sample of data.

00:25:18.500 --> 00:25:21.220
Your classifier C1 had a 5050 chance of

00:25:21.220 --> 00:25:22.910
getting it right by construction.

00:25:22.980 --> 00:25:23.150
Right.

00:25:23.880 --> 00:25:25.640
Then you train C2.

00:25:27.060 --> 00:25:29.590
To try to like do well on this new

00:25:29.590 --> 00:25:30.560
distribution.

00:25:30.560 --> 00:25:32.590
So C2 has like a more difficult job,

00:25:32.590 --> 00:25:33.970
it's going to focus on the things that

00:25:33.970 --> 00:25:35.240
C1 found more difficult.

00:25:37.140 --> 00:25:39.250
Then finally you take all the samples

00:25:39.250 --> 00:25:41.830
that C1 and C2 disagree on, and you

00:25:41.830 --> 00:25:43.590
train a third week learner 1/3

00:25:43.590 --> 00:25:45.740
classifier just on those examples.

00:25:46.420 --> 00:25:49.470
And then at the end you take an average

00:25:49.470 --> 00:25:50.500
of those votes.

00:25:50.500 --> 00:25:52.621
So basically you have like you have

00:25:52.621 --> 00:25:54.050
like one person who's making a

00:25:54.050 --> 00:25:54.740
prediction.

00:25:55.810 --> 00:25:57.946
You take half the predictions that

00:25:57.946 --> 00:26:00.770
person made incorrect and half that

00:26:00.770 --> 00:26:02.320
were correct, and then you get a second

00:26:02.320 --> 00:26:04.192
person to make predictions just looking

00:26:04.192 --> 00:26:05.690
at that at those samples.

00:26:06.470 --> 00:26:08.130
Then you get a third person to be the

00:26:08.130 --> 00:26:09.915
tiebreaker between the first two people

00:26:09.915 --> 00:26:11.440
if they made if they had different

00:26:11.440 --> 00:26:13.320
answers, and then you take a vote of

00:26:13.320 --> 00:26:14.790
those three people as you're finally

00:26:14.790 --> 00:26:15.160
answer.

00:26:16.780 --> 00:26:18.590
Where you can substitute classifier for

00:26:18.590 --> 00:26:19.290
people.

00:26:20.660 --> 00:26:22.100
So this is the boosting idea.

00:26:23.100 --> 00:26:25.120
Now this actually became much more

00:26:25.120 --> 00:26:27.000
popular when it was generalized a

00:26:27.000 --> 00:26:28.480
little bit into this method called

00:26:28.480 --> 00:26:31.450
Adaboost, which stands for adaptive

00:26:31.450 --> 00:26:31.970
boosting.

00:26:33.210 --> 00:26:33.650
So.

00:26:34.390 --> 00:26:38.710
The in adaptive boosting, instead of

00:26:38.710 --> 00:26:42.940
justice directly sampling the data, you

00:26:42.940 --> 00:26:44.730
assign a weight to the data.

00:26:44.730 --> 00:26:46.640
And I'll explain in the next slide, I

00:26:46.640 --> 00:26:48.564
think more of what it means to like

00:26:48.564 --> 00:26:49.860
weight the data when you're doing

00:26:49.860 --> 00:26:50.850
parameter estimation.

00:26:52.360 --> 00:26:55.200
But you assign assign new weights to

00:26:55.200 --> 00:26:57.357
the data so that under that

00:26:57.357 --> 00:27:00.036
distribution the previous weak learner,

00:27:00.036 --> 00:27:02.140
the previous classifier has chance

00:27:02.140 --> 00:27:04.150
accuracy at that weighted distribution.

00:27:04.920 --> 00:27:07.775
So this was one way of doing achieving

00:27:07.775 --> 00:27:10.010
the same thing where you just you draw

00:27:10.010 --> 00:27:12.390
like whole samples so that the previous

00:27:12.390 --> 00:27:14.150
week learner had a 5050 chance of

00:27:14.150 --> 00:27:16.000
getting those samples correct.

00:27:16.830 --> 00:27:18.540
But you can instead assign a softer

00:27:18.540 --> 00:27:20.510
weight to just say that some samples

00:27:20.510 --> 00:27:23.160
matter more than others, so that on the

00:27:23.160 --> 00:27:24.950
distribution the previous classifier

00:27:24.950 --> 00:27:26.330
has a 5050 chance.

00:27:27.900 --> 00:27:30.680
Then you train a new classifier on the

00:27:30.680 --> 00:27:31.820
reweighted samples.

00:27:32.440 --> 00:27:33.350
And then you iterate.

00:27:33.350 --> 00:27:34.800
So then you reweigh them again and

00:27:34.800 --> 00:27:36.340
train a new classifier and keep doing

00:27:36.340 --> 00:27:36.850
that.

00:27:36.850 --> 00:27:38.870
And then at the end you take a weighted

00:27:38.870 --> 00:27:41.560
vote of all of the weak classifiers as

00:27:41.560 --> 00:27:42.510
your final predictor.

00:27:43.430 --> 00:27:47.810
So each each sample is going to each

00:27:47.810 --> 00:27:49.600
classifier is going to try to correct

00:27:49.600 --> 00:27:50.760
the mistakes of the previous

00:27:50.760 --> 00:27:53.090
classifiers, and then all of their

00:27:53.090 --> 00:27:54.650
predictions are combined.

00:27:55.920 --> 00:27:57.240
So I'm going to show a specific

00:27:57.240 --> 00:27:59.650
algorithm in a moment, but first I want

00:27:59.650 --> 00:28:00.520
to clarify.

00:28:01.450 --> 00:28:03.610
What it means to take A to do, like a

00:28:03.610 --> 00:28:05.880
weighted estimation or weighting your

00:28:05.880 --> 00:28:06.720
training samples.

00:28:07.560 --> 00:28:09.600
So essentially it just means that some

00:28:09.600 --> 00:28:11.795
samples count more than others towards

00:28:11.795 --> 00:28:13.780
your parameter estimation or your

00:28:13.780 --> 00:28:14.660
learning objective.

00:28:15.410 --> 00:28:17.500
So let's say that we're trying to build

00:28:17.500 --> 00:28:19.880
a naive Bayes classifier, and so we

00:28:19.880 --> 00:28:21.870
need to estimate the probability that

00:28:21.870 --> 00:28:24.745
some feature is equal to 0 given that

00:28:24.745 --> 00:28:26.130
the label is equal to 0.

00:28:26.130 --> 00:28:28.200
That's like one of the parameters of

00:28:28.200 --> 00:28:28.940
our model.

00:28:29.960 --> 00:28:32.250
If we have an unweighted distribution,

00:28:32.250 --> 00:28:35.940
then that would be a count of how many

00:28:35.940 --> 00:28:39.290
times the feature is equal to 0 and the

00:28:39.290 --> 00:28:40.440
label is equal to 0.

00:28:41.070 --> 00:28:43.380
Divided by a count of how many times

00:28:43.380 --> 00:28:45.290
the label is equal to 0, right?

00:28:45.290 --> 00:28:47.489
So that's probability of X&Y

00:28:47.490 --> 00:28:49.112
essentially divided by probability of

00:28:49.112 --> 00:28:49.380
Y.

00:28:51.950 --> 00:28:53.940
Times north on the numerator and

00:28:53.940 --> 00:28:54.720
denominator.

00:28:56.520 --> 00:28:58.780
Then if I want to take a weighted

00:28:58.780 --> 00:29:01.430
sample, if I wanted an estimate of a

00:29:01.430 --> 00:29:03.490
weighted distribution, I have a weight

00:29:03.490 --> 00:29:04.840
assigned to each of these training

00:29:04.840 --> 00:29:07.570
samples, and that's often done so that

00:29:07.570 --> 00:29:11.140
the weights sum up to one, but it

00:29:11.140 --> 00:29:12.619
doesn't have to be, but they have to be

00:29:12.620 --> 00:29:13.240
non negative.

00:29:15.290 --> 00:29:16.950
OK, so I have to wait for each of these

00:29:16.950 --> 00:29:18.973
samples that says how important it is.

00:29:18.973 --> 00:29:20.940
So when I count the number of times

00:29:20.940 --> 00:29:25.320
that X n = 0 and Y n = 0, then I am

00:29:25.320 --> 00:29:27.200
waiting those counts by won.

00:29:27.200 --> 00:29:29.140
So it's the sum of the weights where

00:29:29.140 --> 00:29:31.185
for the samples in which this condition

00:29:31.185 --> 00:29:33.698
is true divided by the sum of the

00:29:33.698 --> 00:29:35.886
weights for which YN is equal to 0.

00:29:35.886 --> 00:29:37.649
So that's my weighted estimate of that

00:29:37.650 --> 00:29:38.260
statistic.

00:29:40.910 --> 00:29:41.470
Right.

00:29:41.470 --> 00:29:42.960
So it's your turn.

00:29:44.180 --> 00:29:46.470
Let's say that we have this table here.

00:29:46.470 --> 00:29:48.810
So we've got weights on the left side,

00:29:48.810 --> 00:29:51.850
X in the middle, Y and the right, and

00:29:51.850 --> 00:29:53.735
I'm trying to estimate probability of X

00:29:53.735 --> 00:29:55.440
= 0 given y = 0.

00:29:56.140 --> 00:29:57.950
So I'll give you a moment to think

00:29:57.950 --> 00:29:58.690
about it.

00:29:58.690 --> 00:30:00.590
First, what is the unweighted

00:30:00.590 --> 00:30:03.040
distribution and then what is the

00:30:03.040 --> 00:30:04.380
weighted distribution?

00:30:12.540 --> 00:30:13.100
Right.

00:30:20.290 --> 00:30:21.170
Me too.

00:30:21.170 --> 00:30:23.410
My daughter woke me up at 4:00 AM and I

00:30:23.410 --> 00:30:24.700
couldn't fall back asleep.

00:30:39.450 --> 00:30:41.990
I'll I will go through these are the

00:30:41.990 --> 00:30:43.920
examples, so I'll go through it.

00:30:45.400 --> 00:30:45.930
Alright.

00:30:48.690 --> 00:30:50.650
Going, I'll step through it in a

00:30:50.650 --> 00:30:50.930
moment.

00:30:52.270 --> 00:30:53.404
Alright, so let's do the.

00:30:53.404 --> 00:30:55.090
Let's do the unweighted first.

00:30:56.800 --> 00:31:00.940
So how many times does X equal 0 and y

00:31:00.940 --> 00:31:01.480
= 0?

00:31:03.440 --> 00:31:05.030
Right, three.

00:31:05.030 --> 00:31:06.350
OK, so I'm going to have three on the

00:31:06.350 --> 00:31:09.665
numerator and how many times does y =

00:31:09.665 --> 00:31:10.120
0?

00:31:12.070 --> 00:31:13.000
OK, right.

00:31:13.000 --> 00:31:15.710
So unweighted is going to be 3 out of

00:31:15.710 --> 00:31:16.500
five, right?

00:31:18.560 --> 00:31:20.470
Now let's do the weighted.

00:31:20.470 --> 00:31:22.990
So what's the sum of the weights where

00:31:22.990 --> 00:31:25.309
X = 0 and y = 0?

00:31:31.640 --> 00:31:35.026
So there's three rows where X = 0 and y

00:31:35.026 --> 00:31:35.619
= 0.

00:31:36.360 --> 00:31:36.830
Right.

00:31:39.410 --> 00:31:40.990
Right, yeah, three.

00:31:40.990 --> 00:31:42.742
So there's just these three rows, and

00:31:42.742 --> 00:31:44.230
there's a .1 for each of them.

00:31:44.940 --> 00:31:46.030
So that's .3.

00:31:46.800 --> 00:31:49.830
And what is the total weight for y = 0?

00:31:51.710 --> 00:31:52.960
Right .7.

00:31:54.060 --> 00:31:55.960
So the weighted distribution.

00:31:55.960 --> 00:31:57.456
My estimate on the weighted

00:31:57.456 --> 00:31:58.920
distribution is 3 out of seven.

00:32:00.000 --> 00:32:01.120
So that's how it works.

00:32:01.830 --> 00:32:04.770
And if you had so a lot of times we are

00:32:04.770 --> 00:32:06.260
just estimating counts like this.

00:32:06.260 --> 00:32:08.500
If we were training a shorter tree for

00:32:08.500 --> 00:32:11.148
example, then we would be estimating

00:32:11.148 --> 00:32:13.330
the probability of each class within

00:32:13.330 --> 00:32:14.920
the leaf node, which would just be by

00:32:14.920 --> 00:32:15.380
counting.

00:32:17.040 --> 00:32:18.980
Other times, if you're doing like

00:32:18.980 --> 00:32:21.515
logistic regression or had some other

00:32:21.515 --> 00:32:24.000
kind of training or neural network,

00:32:24.000 --> 00:32:26.660
then usually these weights would show

00:32:26.660 --> 00:32:28.410
up as some kind of like weight on the

00:32:28.410 --> 00:32:29.140
loss.

00:32:29.140 --> 00:32:31.290
So we're going to talk about a

00:32:31.290 --> 00:32:32.740
sarcastic gradient descent.

00:32:33.750 --> 00:32:35.110
Starting in the next class.

00:32:35.720 --> 00:32:37.725
And a higher weight would just be like

00:32:37.725 --> 00:32:39.440
a direct multiple on how much you

00:32:39.440 --> 00:32:42.230
adjust your model parameters.

00:32:45.810 --> 00:32:47.920
So here's a specific algorithm called

00:32:47.920 --> 00:32:49.040
Adaboost.

00:32:49.440 --> 00:32:52.289
A real boost, I mean, there's like a

00:32:52.290 --> 00:32:53.816
ton of boosting algorithms.

00:32:53.816 --> 00:32:56.037
There's like discrete ETA boost, real

00:32:56.037 --> 00:32:57.695
boost, logic boost.

00:32:57.695 --> 00:32:59.186
I don't know.

00:32:59.186 --> 00:33:01.880
There's like literally like probably 50

00:33:01.880 --> 00:33:02.260
of them.

00:33:03.670 --> 00:33:05.660
But here's one of the mainstays.

00:33:05.660 --> 00:33:08.930
So you start with the weights being

00:33:08.930 --> 00:33:09.560
uniform.

00:33:09.560 --> 00:33:11.700
They're one over north with N samples.

00:33:11.700 --> 00:33:13.240
Then you're going to train M

00:33:13.240 --> 00:33:14.160
classifiers.

00:33:14.910 --> 00:33:17.605
You fit the classifier to obtain a

00:33:17.605 --> 00:33:19.690
probability estimate, the probability

00:33:19.690 --> 00:33:22.630
of the label being one based on the

00:33:22.630 --> 00:33:23.620
weighted distribution.

00:33:24.500 --> 00:33:26.130
So again, if you're doing trees, this

00:33:26.130 --> 00:33:28.460
would be the fraction of samples in

00:33:28.460 --> 00:33:30.040
each leaf node of the trees where the

00:33:30.040 --> 00:33:31.000
label is equal to 1.

00:33:31.850 --> 00:33:33.530
And where you'd be using a weighted

00:33:33.530 --> 00:33:35.530
sample to compute that fraction, just

00:33:35.530 --> 00:33:36.580
like we did in the last slide.

00:33:37.750 --> 00:33:39.860
Then the prediction of this the score

00:33:39.860 --> 00:33:43.369
essentially for the label one is this

00:33:43.370 --> 00:33:44.110
logic.

00:33:44.110 --> 00:33:47.960
It's the log probability of the label

00:33:47.960 --> 00:33:50.240
being one over the probability not

00:33:50.240 --> 00:33:51.943
being one, which is 1 minus the

00:33:51.943 --> 00:33:52.892
probability of it being one.

00:33:52.892 --> 00:33:54.470
This is for binary classifier.

00:33:55.650 --> 00:33:57.570
That's 1/2 of that logic value.

00:33:58.780 --> 00:34:03.040
And then I re weight the samples and I

00:34:03.040 --> 00:34:05.330
take the previous weight of each sample

00:34:05.330 --> 00:34:07.240
and I multiply it by east to the

00:34:07.240 --> 00:34:09.440
negative yiff FMX.

00:34:09.440 --> 00:34:11.047
So this again is a score.

00:34:11.047 --> 00:34:13.370
So this score defined this way, if it's

00:34:13.370 --> 00:34:15.260
greater than zero that means that.

00:34:16.090 --> 00:34:21.220
If Y ifm is greater than zero, here Yi

00:34:21.220 --> 00:34:24.144
is either -, 1 or one, so -, 1 is the

00:34:24.144 --> 00:34:25.900
negative label, one is the positive

00:34:25.900 --> 00:34:26.200
label.

00:34:26.910 --> 00:34:28.484
If this is greater than zero, that

00:34:28.484 --> 00:34:30.449
means that I'm correct, and if it's

00:34:30.450 --> 00:34:31.969
less than zero it means that I'm

00:34:31.970 --> 00:34:32.960
incorrect.

00:34:32.960 --> 00:34:34.846
So if I predict a score of 1, it means

00:34:34.846 --> 00:34:36.540
that I think it's positive.

00:34:36.540 --> 00:34:40.597
But if the label is -, 1, then Y ifm is

00:34:40.597 --> 00:34:41.850
-, 1, so.

00:34:44.620 --> 00:34:48.350
So this negative Y ifm, if I'm correct

00:34:48.350 --> 00:34:49.990
this is going to be less than one

00:34:49.990 --> 00:34:53.450
because this is going to be east to the

00:34:53.450 --> 00:34:54.860
negative sum value.

00:34:55.970 --> 00:34:57.700
And if I'm incorrect, this is going to

00:34:57.700 --> 00:34:58.600
be greater than one.

00:34:59.270 --> 00:35:00.993
So if I'm correct, the weight is going

00:35:00.993 --> 00:35:03.141
to go down, and if I'm incorrect the

00:35:03.141 --> 00:35:04.070
weight is going to go up.

00:35:04.830 --> 00:35:06.650
And if I'm like confidently correct,

00:35:06.650 --> 00:35:07.908
then the way it's going to go down a

00:35:07.908 --> 00:35:08.156
lot.

00:35:08.156 --> 00:35:09.835
And if I'm confidently incorrect then

00:35:09.835 --> 00:35:10.960
the weight is going to go up a lot.

00:35:12.410 --> 00:35:13.480
That's kind of intuitive.

00:35:14.120 --> 00:35:15.470
And then I just reweigh.

00:35:15.470 --> 00:35:17.630
I just sum my.

00:35:18.910 --> 00:35:19.480
My weight.

00:35:19.480 --> 00:35:22.050
I renormalize my weights, so I make it

00:35:22.050 --> 00:35:23.460
so that the weights sum to one by

00:35:23.460 --> 00:35:24.479
dividing by the sum.

00:35:25.980 --> 00:35:27.630
So then I just iterate, then I train

00:35:27.630 --> 00:35:29.235
new classifier and the way distribution

00:35:29.235 --> 00:35:31.430
recompute this, recompute the weights,

00:35:31.430 --> 00:35:33.300
do that say 20 times.

00:35:33.910 --> 00:35:36.642
And then at the end my classifier is.

00:35:36.642 --> 00:35:38.607
My total score for the classifier is

00:35:38.607 --> 00:35:40.430
the sum of the individual classifier

00:35:40.430 --> 00:35:40.840
scores.

00:35:42.130 --> 00:35:43.300
So it's not too complicated.

00:35:44.220 --> 00:35:47.163
That theory is somewhat complicated, so

00:35:47.163 --> 00:35:49.310
the derivation of why this is the right

00:35:49.310 --> 00:35:51.240
answer and what it's minimizing, and

00:35:51.240 --> 00:35:52.500
that it's like doing with just

00:35:52.500 --> 00:35:54.840
aggression, et cetera, that's all a

00:35:54.840 --> 00:35:56.960
little bit more complicated, but it's

00:35:56.960 --> 00:35:58.250
well worth reading if you're

00:35:58.250 --> 00:35:58.660
interested.

00:35:58.660 --> 00:36:00.046
So there's a link here.

00:36:00.046 --> 00:36:02.085
This is my favorite boosting paper,

00:36:02.085 --> 00:36:03.780
that out of logistic regression paper.

00:36:04.510 --> 00:36:07.660
But this paper is also probably a good

00:36:07.660 --> 00:36:08.080
one to read.

00:36:08.080 --> 00:36:11.440
First, the intro to boosting by friend

00:36:11.440 --> 00:36:12.040
and Shapiro.

00:36:16.960 --> 00:36:18.910
So we can use this with trees.

00:36:18.910 --> 00:36:21.420
We initialize the weights to be

00:36:21.420 --> 00:36:22.190
uniform.

00:36:22.190 --> 00:36:24.250
Then for each tree, usually you do like

00:36:24.250 --> 00:36:24.840
maybe 20.

00:36:25.520 --> 00:36:27.740
You train a small tree this time.

00:36:28.880 --> 00:36:31.370
So you want to train a small tree,

00:36:31.370 --> 00:36:33.550
because the idea of boosting is that

00:36:33.550 --> 00:36:36.020
you're going to reduce the variance by

00:36:36.020 --> 00:36:38.270
having each subsequent classifier fix

00:36:38.270 --> 00:36:39.810
the mistakes of the previous ones.

00:36:40.880 --> 00:36:44.580
So in random forests you have high

00:36:44.580 --> 00:36:46.730
variance, low bias classifiers that

00:36:46.730 --> 00:36:49.650
you've averaged to get low biased low

00:36:49.650 --> 00:36:50.490
variance classifiers.

00:36:51.170 --> 00:36:53.560
In boosting you have low variance, high

00:36:53.560 --> 00:36:56.400
bias classifiers that you incrementally

00:36:56.400 --> 00:36:58.730
train to end up with a low biased, low

00:36:58.730 --> 00:36:59.580
variance classifier.

00:37:01.600 --> 00:37:04.470
So you the tree to a depth, typically

00:37:04.470 --> 00:37:05.620
two to four.

00:37:05.620 --> 00:37:07.960
So often it might sound silly, but

00:37:07.960 --> 00:37:09.690
often you only choose one feature and

00:37:09.690 --> 00:37:11.096
split based on that, and you just have

00:37:11.096 --> 00:37:13.020
like the shortest tree possible, a tree

00:37:13.020 --> 00:37:16.050
with two leaf nodes, and you train 200

00:37:16.050 --> 00:37:16.910
of these trees.

00:37:17.600 --> 00:37:19.975
That actually is surprisingly it works.

00:37:19.975 --> 00:37:22.810
It works quite well, but you might

00:37:22.810 --> 00:37:23.840
train deeper trees.

00:37:25.890 --> 00:37:28.880
So I've used this method for predicting

00:37:28.880 --> 00:37:31.400
like whether pixels belong to the

00:37:31.400 --> 00:37:34.300
ground or sky or et cetera, and I had

00:37:34.300 --> 00:37:37.945
like trees that were of death three and

00:37:37.945 --> 00:37:39.180
I trained 20 trees.

00:37:40.810 --> 00:37:43.480
You estimate you estimate logic

00:37:43.480 --> 00:37:44.810
prediction at each leaf node.

00:37:44.810 --> 00:37:46.840
So just based on the count of how many

00:37:46.840 --> 00:37:48.860
times each class appears in each leaf

00:37:48.860 --> 00:37:50.780
node, reweigh the samples and repeat.

00:37:52.060 --> 00:37:53.780
And then at the end you have the

00:37:53.780 --> 00:37:55.290
prediction is the sum of the logic

00:37:55.290 --> 00:37:56.610
predictions from all the trees.

00:37:59.890 --> 00:38:02.470
So this is a.

00:38:03.810 --> 00:38:07.490
There's like one study by there's a

00:38:07.490 --> 00:38:09.590
couple of studies by Caruana of

00:38:09.590 --> 00:38:11.110
comparing different machine learning

00:38:11.110 --> 00:38:11.600
methods.

00:38:12.320 --> 00:38:14.720
On a bunch of different datasets, so

00:38:14.720 --> 00:38:16.660
this one is from 2006.

00:38:17.480 --> 00:38:20.300
So these are all different data sets.

00:38:20.300 --> 00:38:21.750
It's not too important what they are.

00:38:22.950 --> 00:38:24.610
In this case, they're kind of smaller

00:38:24.610 --> 00:38:26.470
data sets, not too not too many

00:38:26.470 --> 00:38:27.890
samples, not too many features.

00:38:28.620 --> 00:38:31.520
And the scores are normalized so that

00:38:31.520 --> 00:38:34.040
one is like the best achievable score

00:38:34.040 --> 00:38:37.130
and I guess zero would be like chance.

00:38:37.130 --> 00:38:39.940
So that way you can average the

00:38:39.940 --> 00:38:41.890
performance across different data sets

00:38:41.890 --> 00:38:43.300
in a more meaningful way than if you

00:38:43.300 --> 00:38:44.660
were just averaging their errors.

00:38:46.020 --> 00:38:47.760
So here this is like a normalized

00:38:47.760 --> 00:38:50.200
accuracy, so higher is better.

00:38:51.260 --> 00:38:54.700
And then this BTDT is boosted decision

00:38:54.700 --> 00:38:56.760
tree, our F is random forest and north

00:38:56.760 --> 00:38:59.020
is neural network, Ann SVM, which we'll

00:38:59.020 --> 00:39:01.420
talk about Thursday night Bayes,

00:39:01.420 --> 00:39:02.630
logistic regression.

00:39:02.630 --> 00:39:05.580
So Naive Bayes is like pulling up the

00:39:05.580 --> 00:39:06.980
rear, not doing so well.

00:39:06.980 --> 00:39:08.055
It's at the very bottom.

00:39:08.055 --> 00:39:10.236
The district regression is just above

00:39:10.236 --> 00:39:10.588
that.

00:39:10.588 --> 00:39:12.370
Decision trees are just above that.

00:39:13.160 --> 00:39:14.890
And then boosted stumps.

00:39:14.890 --> 00:39:17.130
If you train a very shallow tree that

00:39:17.130 --> 00:39:19.540
only has one feature in each tree,

00:39:19.540 --> 00:39:20.810
that's the next best.

00:39:20.810 --> 00:39:22.010
It's actually pretty similar to

00:39:22.010 --> 00:39:22.930
logistic regression.

00:39:24.050 --> 00:39:29.110
K&N near neural networks SVMS.

00:39:29.760 --> 00:39:32.860
And then the top is boosted decision

00:39:32.860 --> 00:39:33.940
trees and random forests.

00:39:34.680 --> 00:39:36.440
And there's different versions of this,

00:39:36.440 --> 00:39:37.903
which is just like different ways of

00:39:37.903 --> 00:39:39.130
trying to calibrate your final

00:39:39.130 --> 00:39:40.550
prediction, which means trying to make

00:39:40.550 --> 00:39:41.890
it better fit of probability.

00:39:41.890 --> 00:39:44.055
But that's not our topic for now, so

00:39:44.055 --> 00:39:45.290
that's kind of ignorable.

00:39:46.110 --> 00:39:48.350
Main the main conclusion is that in

00:39:48.350 --> 00:39:50.690
this competition among classifiers.

00:39:51.340 --> 00:39:54.690
Boosted decision trees is #1 and

00:39:54.690 --> 00:39:56.950
following very close behind is random

00:39:56.950 --> 00:39:58.810
forests with almost the same average

00:39:58.810 --> 00:39:59.180
score.

00:40:00.070 --> 00:40:01.890
So these two ensemble methods of trees

00:40:01.890 --> 00:40:03.070
are the two best methods.

00:40:04.040 --> 00:40:05.030
According to the study.

00:40:06.160 --> 00:40:07.990
Then in 2008 they did another

00:40:07.990 --> 00:40:11.110
comparison on high dimensional data.

00:40:12.360 --> 00:40:14.570
So here they had the features range

00:40:14.570 --> 00:40:17.900
from around 700 features to 685,000

00:40:17.900 --> 00:40:18.870
features.

00:40:19.750 --> 00:40:21.540
This is like IMDb where you're trying

00:40:21.540 --> 00:40:25.490
to predict the rating of movies.

00:40:25.490 --> 00:40:28.750
I think spam classification and other

00:40:28.750 --> 00:40:29.210
problems.

00:40:30.100 --> 00:40:32.340
And then again, they're comparing the

00:40:32.340 --> 00:40:33.460
different approaches.

00:40:33.460 --> 00:40:36.675
So again, boosted decision trees gets

00:40:36.675 --> 00:40:38.400
the best score on average.

00:40:38.400 --> 00:40:41.030
I don't know exactly how the weighting

00:40:41.030 --> 00:40:42.480
is done here, they can be greater than

00:40:42.480 --> 00:40:42.580
one.

00:40:43.270 --> 00:40:45.410
But boosted decision trees probably

00:40:45.410 --> 00:40:46.963
compared to some baseline boosted

00:40:46.963 --> 00:40:48.610
decision trees gets the best score on

00:40:48.610 --> 00:40:49.340
average.

00:40:49.340 --> 00:40:51.650
And random forests is number 2.

00:40:51.650 --> 00:40:53.660
Again, it's naive Bayes on the bottom.

00:40:53.750 --> 00:40:54.210


00:40:55.000 --> 00:40:56.420
Logistic regression does a bit better

00:40:56.420 --> 00:40:57.780
and this high dimensional data.

00:40:57.780 --> 00:40:59.420
Again, linear classifiers are more

00:40:59.420 --> 00:41:00.950
powerful when you have more features,

00:41:00.950 --> 00:41:03.980
but still not outperforming their

00:41:03.980 --> 00:41:05.750
neural networks or SVM or random

00:41:05.750 --> 00:41:06.140
forests.

00:41:07.950 --> 00:41:10.620
But also, even though boosted decision

00:41:10.620 --> 00:41:13.070
trees did the best on average, they're

00:41:13.070 --> 00:41:15.150
not doing so when you have tons of

00:41:15.150 --> 00:41:15.940
features.

00:41:15.940 --> 00:41:17.926
They're random forest is doing the

00:41:17.926 --> 00:41:18.189
best.

00:41:19.490 --> 00:41:22.200
And the reason for that is that boosted

00:41:22.200 --> 00:41:27.580
decision trees have a weakness of that.

00:41:27.810 --> 00:41:29.700
High.

00:41:29.770 --> 00:41:30.380


00:41:31.500 --> 00:41:31.932
They have.

00:41:31.932 --> 00:41:33.480
They have a weakness of tending to

00:41:33.480 --> 00:41:35.100
overfit the data if they've got too

00:41:35.100 --> 00:41:36.210
much flexibility.

00:41:36.210 --> 00:41:39.049
So if you have 600,000 features and

00:41:39.050 --> 00:41:40.512
you're trying to just fix the mistakes

00:41:40.512 --> 00:41:42.930
of the previous classifier iteratively,

00:41:42.930 --> 00:41:44.400
then there's a pretty good chance that

00:41:44.400 --> 00:41:45.840
you could fix those mistakes for the

00:41:45.840 --> 00:41:46.365
wrong reason.

00:41:46.365 --> 00:41:47.970
And so they tend to be.

00:41:47.970 --> 00:41:49.847
When you have a lot of features, you

00:41:49.847 --> 00:41:52.596
end up with high, high variance, high

00:41:52.596 --> 00:41:55.186
bias features that you then reduce the

00:41:55.186 --> 00:41:57.588
variance of, but you still end up with

00:41:57.588 --> 00:41:59.840
high variance, low bias features

00:41:59.840 --> 00:42:00.710
classifiers.

00:42:05.030 --> 00:42:07.480
So just to recap that boosted decision

00:42:07.480 --> 00:42:09.150
trees and random forests work for

00:42:09.150 --> 00:42:10.063
different reasons.

00:42:10.063 --> 00:42:12.345
Boosted trees use a lot of small trees

00:42:12.345 --> 00:42:14.430
to iteratively refine the prediction,

00:42:14.430 --> 00:42:16.445
and combining the prediction from many

00:42:16.445 --> 00:42:18.020
trees reduces the bias.

00:42:18.020 --> 00:42:20.380
But they have a danger of overfitting

00:42:20.380 --> 00:42:22.717
if you have too many trees, or the

00:42:22.717 --> 00:42:24.640
trees are too big or you have too many

00:42:24.640 --> 00:42:25.160
features.

00:42:25.820 --> 00:42:28.470
Then they may not generalize that well.

00:42:29.740 --> 00:42:32.170
Random forests used big trees, which

00:42:32.170 --> 00:42:34.050
are low bias and high variance.

00:42:34.050 --> 00:42:36.000
They average a lot of those tree

00:42:36.000 --> 00:42:38.303
predictions, which reduces the

00:42:38.303 --> 00:42:40.170
variance, and it's kind of hard to make

00:42:40.170 --> 00:42:41.079
them not work.

00:42:41.080 --> 00:42:42.900
They're not always like the very best

00:42:42.900 --> 00:42:46.320
thing you can do, but they always, as

00:42:46.320 --> 00:42:48.240
far as I can see and I've ever seen,

00:42:48.240 --> 00:42:49.810
they always work like at least pretty

00:42:49.810 --> 00:42:50.110
well.

00:42:51.130 --> 00:42:52.790
As long as you just train enough trees.

00:42:55.870 --> 00:42:56.906
Ensemble.

00:42:56.906 --> 00:43:00.090
There's other kinds of ensembles too,

00:43:00.090 --> 00:43:01.635
so you can average the predictions of

00:43:01.635 --> 00:43:03.280
any classifiers as long as they're not

00:43:03.280 --> 00:43:04.210
duplicates of each other.

00:43:04.210 --> 00:43:05.323
If they're duplicates of each other,

00:43:05.323 --> 00:43:07.150
you don't get any benefit, obviously,

00:43:07.150 --> 00:43:08.260
because they'll just make the same

00:43:08.260 --> 00:43:08.720
prediction.

00:43:10.000 --> 00:43:12.170
So you can also apply this to deep

00:43:12.170 --> 00:43:13.510
neural networks, for example.

00:43:13.510 --> 00:43:15.650
So here is something showing that

00:43:15.650 --> 00:43:19.120
cascades and averages on average

00:43:19.120 --> 00:43:21.430
ensembles of classifiers outperform

00:43:21.430 --> 00:43:23.260
single classifiers even when you're

00:43:23.260 --> 00:43:25.470
considering the computation required

00:43:25.470 --> 00:43:26.110
for them.

00:43:27.550 --> 00:43:29.460
And a cascade is when you train one

00:43:29.460 --> 00:43:30.340
classifier.

00:43:31.050 --> 00:43:34.512
And then you let it make its confident

00:43:34.512 --> 00:43:36.180
decisions, and then subsequent

00:43:36.180 --> 00:43:38.240
classifiers only make decisions about

00:43:38.240 --> 00:43:39.280
the less confident.

00:43:40.500 --> 00:43:41.660
Examples.

00:43:41.660 --> 00:43:42.870
And then you keep on doing that.

00:43:46.120 --> 00:43:49.770
Let me give you a two-minute stretch

00:43:49.770 --> 00:43:51.430
break before I go into a detailed

00:43:51.430 --> 00:43:53.670
example of using random forests.

00:43:54.690 --> 00:43:56.620
And you can think about this question

00:43:56.620 --> 00:43:57.220
if you want.

00:43:57.920 --> 00:44:00.120
So suppose you had an infinite size

00:44:00.120 --> 00:44:03.100
audience and where and they could

00:44:03.100 --> 00:44:04.100
choose ABCD.

00:44:05.500 --> 00:44:07.120
What is the situation where you're

00:44:07.120 --> 00:44:08.845
guaranteed to have a correct answer?

00:44:08.845 --> 00:44:11.410
What if, let's say, a randomly sampled

00:44:11.410 --> 00:44:12.970
audience member is going to report an

00:44:12.970 --> 00:44:14.800
answer with probability PY?

00:44:15.770 --> 00:44:17.650
What guarantees a correct answer?

00:44:17.650 --> 00:44:19.930
And let's say instead you choose a

00:44:19.930 --> 00:44:21.850
friend which is a random member of the

00:44:21.850 --> 00:44:22.830
audience in this case.

00:44:23.570 --> 00:44:24.900
What's the probability that your

00:44:24.900 --> 00:44:25.930
friend's answer is correct?

00:44:26.560 --> 00:44:28.950
So think about those or don't.

00:44:28.950 --> 00:44:30.280
It's up to you.

00:44:30.280 --> 00:44:31.790
I'll give you the answer in 2 minutes.

00:45:07.040 --> 00:45:09.180
Some people would, they would say like

00:45:09.180 --> 00:45:11.130
cherry or yeah.

00:45:13.980 --> 00:45:14.270
Yeah.

00:45:15.730 --> 00:45:17.400
Or they might be color blind.

00:45:18.390 --> 00:45:18.960
I see.

00:45:24.750 --> 00:45:25.310
That's true.

00:45:29.140 --> 00:45:31.120
It's actually pretty hard not get a

00:45:31.120 --> 00:45:32.550
correct answer, I would say.

00:45:43.340 --> 00:45:46.300
Correct decision wide away look goes

00:45:46.300 --> 00:45:49.670
down because you want the subsequent

00:45:49.670 --> 00:45:51.240
classifiers to focus more on the

00:45:51.240 --> 00:45:52.050
mistakes.

00:45:52.050 --> 00:45:56.300
So if it's incorrect then the weight

00:45:56.300 --> 00:45:57.920
goes up so then it matters more to the

00:45:57.920 --> 00:45:58.730
next classifier.

00:46:02.730 --> 00:46:04.160
Unclassified award goes to.

00:46:06.000 --> 00:46:07.700
It could go back up, yeah.

00:46:10.830 --> 00:46:12.670
The weights keeping being multiplied by

00:46:12.670 --> 00:46:14.500
that factor, so yeah.

00:46:15.520 --> 00:46:15.870
Yeah.

00:46:17.280 --> 00:46:17.700
You're welcome.

00:46:25.930 --> 00:46:27.410
All right, times up.

00:46:28.930 --> 00:46:32.470
So what is like the weakest condition?

00:46:32.470 --> 00:46:34.270
I should have made it a little harder.

00:46:34.270 --> 00:46:35.900
Obviously there's one condition, which

00:46:35.900 --> 00:46:37.450
is that every audience member knows the

00:46:37.450 --> 00:46:37.820
answer.

00:46:37.820 --> 00:46:38.380
That's easy.

00:46:39.350 --> 00:46:41.160
But what's the weakest condition that

00:46:41.160 --> 00:46:43.090
guarantees a correct answer?

00:46:43.090 --> 00:46:45.725
So what has to be true for this answer

00:46:45.725 --> 00:46:47.330
to be correct with an infinite audience

00:46:47.330 --> 00:46:47.710
size?

00:46:52.040 --> 00:46:52.530
Right.

00:46:54.740 --> 00:46:56.290
Yes, one audience member.

00:46:56.290 --> 00:46:57.810
No, that won't work.

00:46:57.810 --> 00:46:59.550
So because then the probability would

00:46:59.550 --> 00:47:03.790
be 0 right of the correct answer if all

00:47:03.790 --> 00:47:05.470
the other audience members thought it

00:47:05.470 --> 00:47:06.280
was a different answer.

00:47:10.760 --> 00:47:12.740
If this size of the audience is one,

00:47:12.740 --> 00:47:14.936
yeah, but you have an infinite size

00:47:14.936 --> 00:47:15.940
audience and the problem.

00:47:18.270 --> 00:47:18.770
Does anybody?

00:47:18.770 --> 00:47:19.940
Yeah.

00:47:23.010 --> 00:47:24.938
Yes, the probability of the correct

00:47:24.938 --> 00:47:26.070
answer has to be the highest.

00:47:26.070 --> 00:47:27.548
So if the probability of the correct

00:47:27.548 --> 00:47:30.714
answer is say 26%, but the probability

00:47:30.714 --> 00:47:33.220
of all the other answers is like just

00:47:33.220 --> 00:47:35.923
under 25%, then you'll get the correct

00:47:35.923 --> 00:47:36.226
answer.

00:47:36.226 --> 00:47:38.578
So even though almost three out of four

00:47:38.578 --> 00:47:41.013
of the audience members can be wrong,

00:47:41.013 --> 00:47:41.569
it's.

00:47:41.570 --> 00:47:43.378
I mean, it's possible for three out of

00:47:43.378 --> 00:47:45.038
four of the audience members to be

00:47:45.038 --> 00:47:46.698
wrong almost, but still get the correct

00:47:46.698 --> 00:47:48.140
answer, still be guaranteed they're

00:47:48.140 --> 00:47:48.760
correct answer.

00:47:50.250 --> 00:47:52.385
If you were to pull the infinite size

00:47:52.385 --> 00:47:53.940
audience, of course with the limited

00:47:53.940 --> 00:47:55.930
audience you also have then variance,

00:47:55.930 --> 00:47:57.800
so you would want a bigger margin to be

00:47:57.800 --> 00:47:58.190
confident.

00:47:59.100 --> 00:48:01.480
And if a friend is a random member of

00:48:01.480 --> 00:48:02.660
the audience, this is an easier

00:48:02.660 --> 00:48:03.270
question.

00:48:03.270 --> 00:48:05.190
Then what's the probability that your

00:48:05.190 --> 00:48:06.290
friend's answer is correct?

00:48:09.150 --> 00:48:09.440
Right.

00:48:10.320 --> 00:48:11.852
Yeah, P of A, yeah.

00:48:11.852 --> 00:48:13.830
So in this setting, so it's possible

00:48:13.830 --> 00:48:15.898
that your friend could only have a 25%

00:48:15.898 --> 00:48:17.650
chance of being correct, but the

00:48:17.650 --> 00:48:19.595
audience has a 100% chance of being

00:48:19.595 --> 00:48:19.859
correct.

00:48:24.800 --> 00:48:26.830
Alright, so I'm going to give a

00:48:26.830 --> 00:48:29.010
detailed example of random forests.

00:48:29.010 --> 00:48:30.950
If you took computational photography

00:48:30.950 --> 00:48:32.850
with me, then you saw this example, but

00:48:32.850 --> 00:48:34.100
now you will see it in a new light.

00:48:34.950 --> 00:48:37.960
And so this is using this is the Kinect

00:48:37.960 --> 00:48:38.490
algorithm.

00:48:38.490 --> 00:48:40.220
So you guys might remember the Kinect

00:48:40.220 --> 00:48:42.740
came out in around 2011.

00:48:43.720 --> 00:48:46.080
For gaming and then was like widely

00:48:46.080 --> 00:48:47.590
adopted by the robotics community

00:48:47.590 --> 00:48:48.270
question.

00:48:56.480 --> 00:48:59.850
Alright, the answer is probability of a

00:48:59.850 --> 00:49:04.080
can be just marginally above 25% and

00:49:04.080 --> 00:49:06.360
the other probabilities are marginally

00:49:06.360 --> 00:49:07.440
below 25%.

00:49:09.310 --> 00:49:09.720
Yeah.

00:49:11.560 --> 00:49:15.050
All right, so the Kinect came out, you

00:49:15.050 --> 00:49:17.280
could play lots of games with it and it

00:49:17.280 --> 00:49:18.570
was also used for robotics.

00:49:18.570 --> 00:49:20.864
But for the games anyway, one of the

00:49:20.864 --> 00:49:22.950
one of the key things they had to solve

00:49:22.950 --> 00:49:23.943
was to.

00:49:23.943 --> 00:49:26.635
So first the Kinect has it does some

00:49:26.635 --> 00:49:28.120
like structured light thing in order to

00:49:28.120 --> 00:49:28.990
get a depth image.

00:49:29.660 --> 00:49:30.550
And then?

00:49:30.720 --> 00:49:31.330
And.

00:49:32.070 --> 00:49:34.040
And then the Kinect needs to estimate

00:49:34.040 --> 00:49:37.000
body purpose given the depth image, so

00:49:37.000 --> 00:49:38.940
that it can tell if you're like dancing

00:49:38.940 --> 00:49:40.810
correctly or doing the sport or

00:49:40.810 --> 00:49:44.000
whatever corresponds to the game.

00:49:45.020 --> 00:49:47.260
So given this depth image, you have to

00:49:47.260 --> 00:49:50.580
try to predict for like what are the

00:49:50.580 --> 00:49:52.300
key points of the body pose.

00:49:52.300 --> 00:49:53.050
That's the problem.

00:49:54.850 --> 00:49:56.840
And they need to do it really fast too,

00:49:56.840 --> 00:49:59.230
because they're because they only get a

00:49:59.230 --> 00:50:02.064
small fraction of the GPU of the Xbox

00:50:02.064 --> 00:50:05.222
to do this, 2% of the GPU of the Xbox

00:50:05.222 --> 00:50:06.740
to do this in real time.

00:50:09.190 --> 00:50:12.370
So the basic algorithm is from.

00:50:12.370 --> 00:50:15.450
This is described in this paper by

00:50:15.450 --> 00:50:16.640
Microsoft Cambridge.

00:50:17.400 --> 00:50:21.430
And the overall the processes, you go

00:50:21.430 --> 00:50:23.180
from a depth image and segment it.

00:50:23.180 --> 00:50:25.950
Then you predict for each pixel which

00:50:25.950 --> 00:50:28.200
of the body parts corresponds to that

00:50:28.200 --> 00:50:29.200
pixel.

00:50:29.200 --> 00:50:30.410
Is it like the right side of the face

00:50:30.410 --> 00:50:31.380
or left side of the face?

00:50:32.180 --> 00:50:34.540
And then you take those predictions and

00:50:34.540 --> 00:50:36.210
combine them to get a key point

00:50:36.210 --> 00:50:36.730
estimate.

00:50:38.490 --> 00:50:39.730
So here's another view of it.

00:50:40.400 --> 00:50:42.905
Given RGB image, that's Jamie shot in

00:50:42.905 --> 00:50:45.846
the first author you then and a depth

00:50:45.846 --> 00:50:46.223
image.

00:50:46.223 --> 00:50:48.120
You don't use the RGB actually, you

00:50:48.120 --> 00:50:49.983
just segment out the body from the

00:50:49.983 --> 00:50:50.199
depth.

00:50:50.200 --> 00:50:51.900
It's like the near pixels.

00:50:52.670 --> 00:50:55.185
And then you label them into parts and

00:50:55.185 --> 00:50:57.790
then you assign the joint positions.

00:51:00.690 --> 00:51:03.489
So the reason this is kind of this is

00:51:03.490 --> 00:51:05.050
pretty hard because you're going to

00:51:05.050 --> 00:51:06.470
have a lot of different bodies and

00:51:06.470 --> 00:51:08.370
orientations and poses and wearing

00:51:08.370 --> 00:51:10.500
different kinds of clothes, and you

00:51:10.500 --> 00:51:12.490
want this to work for everybody because

00:51:12.490 --> 00:51:14.400
if it fails, then the games not any

00:51:14.400 --> 00:51:14.710
fun.

00:51:15.740 --> 00:51:19.610
And So what they did is they collected

00:51:19.610 --> 00:51:22.995
a lot of examples of motion capture

00:51:22.995 --> 00:51:24.990
they had like different people do like

00:51:24.990 --> 00:51:26.970
motion capture and got like real

00:51:26.970 --> 00:51:30.190
examples and then they took those body

00:51:30.190 --> 00:51:33.270
frames and rigged a synthetic models.

00:51:33.940 --> 00:51:35.700
And generated even more synthetic

00:51:35.700 --> 00:51:37.550
examples of people in the same poses.

00:51:38.150 --> 00:51:40.020
And on these synthetic examples, it was

00:51:40.020 --> 00:51:41.945
easy to label the parts because they're

00:51:41.945 --> 00:51:42.450
synthetic.

00:51:42.450 --> 00:51:44.080
So they could just like essentially

00:51:44.080 --> 00:51:46.740
texture the parts and then they would

00:51:46.740 --> 00:51:48.880
know like which pixel corresponds to

00:51:48.880 --> 00:51:49.410
each label.

00:51:51.640 --> 00:51:53.930
So the same this is showing that the

00:51:53.930 --> 00:51:58.010
same body part this wrist or hand here.

00:51:58.740 --> 00:52:00.300
Can look quite different.

00:52:00.300 --> 00:52:02.050
It's the same part in all of these

00:52:02.050 --> 00:52:04.200
images, but depending on where it is

00:52:04.200 --> 00:52:05.700
and how the body is posed, then the

00:52:05.700 --> 00:52:06.820
image looks pretty different.

00:52:06.820 --> 00:52:09.060
So this is a pretty challenging problem

00:52:09.060 --> 00:52:11.590
to know that this pixel in the center

00:52:11.590 --> 00:52:14.520
of the cross is the wrist.

00:52:15.390 --> 00:52:16.090
Where the hand?

00:52:19.180 --> 00:52:21.070
All right, so the thresholding of the

00:52:21.070 --> 00:52:24.640
depth is relatively straightforward.

00:52:24.640 --> 00:52:27.190
And then they need to learn to predict

00:52:27.190 --> 00:52:30.599
for each pixel whether which of the

00:52:30.600 --> 00:52:32.700
possible body parts that pixel

00:52:32.700 --> 00:52:33.510
corresponds to.

00:52:34.910 --> 00:52:37.015
And these really simple features, the

00:52:37.015 --> 00:52:41.500
features are either a an offset feature

00:52:41.500 --> 00:52:43.270
where if you're trying to predict for

00:52:43.270 --> 00:52:46.610
this pixel at the center, here you

00:52:46.610 --> 00:52:49.570
shift some number of pixels that are

00:52:49.570 --> 00:52:51.650
dependent, so some pixels times depth.

00:52:52.360 --> 00:52:54.100
In some direction, and you look at the

00:52:54.100 --> 00:52:55.740
depth of that corresponding pixel,

00:52:55.740 --> 00:52:58.230
which could be like a particular value

00:52:58.230 --> 00:52:59.660
to indicate that it's off the body.

00:53:01.290 --> 00:53:03.020
So if you're at this pixel and you use

00:53:03.020 --> 00:53:05.205
this feature Theta one, then you end up

00:53:05.205 --> 00:53:05.667
over here.

00:53:05.667 --> 00:53:07.144
If you're looking at this pixel then

00:53:07.144 --> 00:53:08.770
you end up on the head over here in

00:53:08.770 --> 00:53:09.450
this example.

00:53:10.350 --> 00:53:12.440
And then you have other features that

00:53:12.440 --> 00:53:14.210
are based on the difference of depths.

00:53:14.210 --> 00:53:16.870
So given some position, you look at 2

00:53:16.870 --> 00:53:19.000
offsets and take the difference of

00:53:19.000 --> 00:53:19.600
those depths.

00:53:21.300 --> 00:53:23.260
And then you can generate like

00:53:23.260 --> 00:53:25.020
basically infinite numbers of those

00:53:25.020 --> 00:53:26.010
features, right?

00:53:26.010 --> 00:53:27.895
There's like a lot of combinations of

00:53:27.895 --> 00:53:29.655
features using different offsets that

00:53:29.655 --> 00:53:30.485
you could create.

00:53:30.485 --> 00:53:32.510
And they also have lots of data, which

00:53:32.510 --> 00:53:34.500
as I mentioned came from mocap and then

00:53:34.500 --> 00:53:35.260
synthetic data.

00:53:36.390 --> 00:53:39.060
And so they train, they train random

00:53:39.060 --> 00:53:42.990
forests based on these features on all

00:53:42.990 --> 00:53:43.640
this data.

00:53:43.640 --> 00:53:45.030
So again, they have millions of

00:53:45.030 --> 00:53:45.900
examples.

00:53:45.900 --> 00:53:47.995
They can like practically infinite

00:53:47.995 --> 00:53:49.680
features, but you'd sample some number

00:53:49.680 --> 00:53:50.930
of features and tree in a tree.

00:53:53.210 --> 00:53:54.500
I think I just explained that.

00:53:56.320 --> 00:53:58.270
Sorry, I got a little ahead of myself,

00:53:58.270 --> 00:54:00.264
but this is just an illustration of

00:54:00.264 --> 00:54:03.808
their training data, 500,000 frames and

00:54:03.808 --> 00:54:07.414
then they got 3D models for 15 bodies

00:54:07.414 --> 00:54:09.990
and then they synthesized all the

00:54:09.990 --> 00:54:11.860
motion capture data on all of those

00:54:11.860 --> 00:54:14.160
bodies to get their training and test

00:54:14.160 --> 00:54:15.319
in synthetic test data.

00:54:16.200 --> 00:54:17.730
So this is showing similar synthetic

00:54:17.730 --> 00:54:18.110
data.

00:54:21.210 --> 00:54:24.110
And then so they so they're classifier

00:54:24.110 --> 00:54:26.500
is a random forest, so again they just.

00:54:26.570 --> 00:54:27.060


00:54:27.830 --> 00:54:31.095
Randomly sample a set of those possible

00:54:31.095 --> 00:54:33.030
features, or generate a set of features

00:54:33.030 --> 00:54:35.700
and randomly subsample their training

00:54:35.700 --> 00:54:36.030
data.

00:54:36.900 --> 00:54:39.315
And then train a tree to completion and

00:54:39.315 --> 00:54:41.810
then each tree or maybe to maximum

00:54:41.810 --> 00:54:42.100
depth.

00:54:42.100 --> 00:54:43.575
In this case you might not change the

00:54:43.575 --> 00:54:44.820
completion since you may have like

00:54:44.820 --> 00:54:45.680
millions of samples.

00:54:46.770 --> 00:54:48.660
But you trained to some depth and then

00:54:48.660 --> 00:54:50.570
each node will have some probability

00:54:50.570 --> 00:54:52.160
estimate for each of the classes.

00:54:52.970 --> 00:54:54.626
And then you generate a new tree and

00:54:54.626 --> 00:54:56.400
you keep on doing that independently.

00:54:57.510 --> 00:54:59.100
And then you at the end you're

00:54:59.100 --> 00:55:01.282
predictor is an average of the

00:55:01.282 --> 00:55:03.230
probabilities, the class probabilities

00:55:03.230 --> 00:55:04.530
that each of the trees predicts.

00:55:05.970 --> 00:55:09.780
So it may sound like at first glance

00:55:09.780 --> 00:55:11.030
when you look at this you might think,

00:55:11.030 --> 00:55:13.530
well this seems really slow you then in

00:55:13.530 --> 00:55:14.880
order to.

00:55:15.410 --> 00:55:16.040
Make a prediction.

00:55:16.040 --> 00:55:17.936
You have to query all of these trees

00:55:17.936 --> 00:55:19.760
and then sum up their responses.

00:55:19.760 --> 00:55:21.940
But when you're implementing an GPU,

00:55:21.940 --> 00:55:23.658
it's actually really fast because these

00:55:23.658 --> 00:55:24.840
can all be done in parallel.

00:55:24.840 --> 00:55:26.334
The trees don't depend on each other,

00:55:26.334 --> 00:55:29.161
so you can do the inference on all the

00:55:29.161 --> 00:55:31.045
trees simultaneously, and you can do

00:55:31.045 --> 00:55:32.120
inference for all the pixels

00:55:32.120 --> 00:55:33.600
simultaneously if you have enough

00:55:33.600 --> 00:55:33.968
memory.

00:55:33.968 --> 00:55:36.919
And so it's actually can be done in

00:55:36.920 --> 00:55:38.225
remarkably fast.

00:55:38.225 --> 00:55:41.300
So they can do this in real time using

00:55:41.300 --> 00:55:43.506
2% of the computational resources of

00:55:43.506 --> 00:55:44.280
the Xbox.

00:55:48.160 --> 00:55:48.770


00:55:49.810 --> 00:55:53.730
And then finally they would get the, so

00:55:53.730 --> 00:55:54.700
I'll show it here.

00:55:54.700 --> 00:55:56.249
So first they are like labeling the

00:55:56.250 --> 00:55:57.465
pixels like this.

00:55:57.465 --> 00:56:01.607
So this is the, sorry, over here the

00:56:01.607 --> 00:56:03.690
Pixel labels can be like a little bit

00:56:03.690 --> 00:56:05.410
of noise, a little bit noisy, but at

00:56:05.410 --> 00:56:07.170
the end they don't need a pixel perfect

00:56:07.170 --> 00:56:09.430
segmentation or pixel perfect labeling.

00:56:10.060 --> 00:56:11.990
What they really care about is the

00:56:11.990 --> 00:56:13.950
position of the joints, the 3D position

00:56:13.950 --> 00:56:14.790
of the joints.

00:56:15.710 --> 00:56:17.899
And so based on the depth and based on

00:56:17.900 --> 00:56:19.416
which pixels are labeled with each

00:56:19.416 --> 00:56:22.290
joint, they can get the average 3D

00:56:22.290 --> 00:56:24.420
position of these labels.

00:56:24.420 --> 00:56:27.280
And then they just put it like slightly

00:56:27.280 --> 00:56:29.070
behind that in a joint dependent way.

00:56:29.070 --> 00:56:31.429
So like if that the average depth of

00:56:31.429 --> 00:56:33.346
these pixels on my shoulder, then that

00:56:33.346 --> 00:56:34.860
the center of my shoulder is going to

00:56:34.860 --> 00:56:36.950
be an inch and 1/2 behind that or

00:56:36.950 --> 00:56:37.619
something like that.

00:56:38.450 --> 00:56:40.600
So then you get the 3D position of my

00:56:40.600 --> 00:56:41.030
shoulder.

00:56:42.480 --> 00:56:44.303
And so even though they're pixel

00:56:44.303 --> 00:56:46.280
predictions might be a little noisy,

00:56:46.280 --> 00:56:48.130
the joint predictions are more accurate

00:56:48.130 --> 00:56:49.550
because they're based on a combination

00:56:49.550 --> 00:56:50.499
of pixel predictions.

00:56:54.090 --> 00:56:55.595
So here is showing the ground truth.

00:56:55.595 --> 00:56:57.360
This is the depth image, this is a

00:56:57.360 --> 00:57:00.160
pixel labels and then this is the joint

00:57:00.160 --> 00:57:00.780
labels.

00:57:01.450 --> 00:57:03.850
And then and.

00:57:03.850 --> 00:57:06.005
This is showing the actual predictions

00:57:06.005 --> 00:57:07.210
and some examples.

00:57:09.420 --> 00:57:11.020
And here you can see the same thing.

00:57:11.020 --> 00:57:13.630
So these are the input depth images.

00:57:14.400 --> 00:57:16.480
This is the pixel predictions on those

00:57:16.480 --> 00:57:17.210
depth images.

00:57:17.860 --> 00:57:19.870
And then this is showing the estimated

00:57:19.870 --> 00:57:22.385
pose from different perspectives so

00:57:22.385 --> 00:57:24.910
that you can see it looks kind of

00:57:24.910 --> 00:57:25.100
right.

00:57:25.100 --> 00:57:26.780
So like in this case for example, it's

00:57:26.780 --> 00:57:28.570
estimating that the person is standing

00:57:28.570 --> 00:57:30.840
with his hands like out and slightly in

00:57:30.840 --> 00:57:31.110
front.

00:57:36.130 --> 00:57:38.440
And you can see if you vary the number

00:57:38.440 --> 00:57:41.810
of training samples, you get like

00:57:41.810 --> 00:57:42.670
pretty good.

00:57:42.670 --> 00:57:45.860
I mean essentially what I would say is

00:57:45.860 --> 00:57:47.239
that you need a lot of training samples

00:57:47.240 --> 00:57:48.980
to do well in this task.

00:57:49.660 --> 00:57:52.330
So as you start to get up to 100,000 or

00:57:52.330 --> 00:57:53.640
a million training samples.

00:57:54.300 --> 00:57:58.360
Your average accuracy gets up to 60%.

00:57:59.990 --> 00:58:02.350
And 60% might not sound that good, but

00:58:02.350 --> 00:58:04.339
it's actually fine because a lot of the

00:58:04.340 --> 00:58:05.930
errors will just be on the margin where

00:58:05.930 --> 00:58:08.050
you're like whether this pixel is the

00:58:08.050 --> 00:58:09.500
upper arm or the shoulder.

00:58:09.500 --> 00:58:13.110
And so the per pixel accuracy of 60%

00:58:13.110 --> 00:58:14.420
gives you pretty accurate joint

00:58:14.420 --> 00:58:15.030
positions.

00:58:16.680 --> 00:58:18.460
One of the surprising things about the

00:58:18.460 --> 00:58:21.979
paper was that the synthetic data was

00:58:21.980 --> 00:58:24.000
so effective because in all past

00:58:24.000 --> 00:58:26.322
research, pretty much when people use

00:58:26.322 --> 00:58:27.720
synthetic data it didn't like

00:58:27.720 --> 00:58:29.700
generalize that did the test data.

00:58:29.700 --> 00:58:30.940
And I think the reason that it

00:58:30.940 --> 00:58:32.580
generalizes well in this case is that

00:58:32.580 --> 00:58:34.830
depth data is a lot easier to simulate

00:58:34.830 --> 00:58:35.290
than.

00:58:35.930 --> 00:58:37.170
RGB data.

00:58:37.170 --> 00:58:39.810
So now people have used RGB data

00:58:39.810 --> 00:58:40.340
somewhat.

00:58:40.340 --> 00:58:43.440
It's often used in autonomous vehicle

00:58:43.440 --> 00:58:46.760
training, but at the time it had not

00:58:46.760 --> 00:58:47.920
really been used effectively.

00:58:58.700 --> 00:58:58.980
OK.

00:59:00.020 --> 00:59:01.500
Is there any questions about that?

00:59:04.850 --> 00:59:06.820
And then the last big thing I want to

00:59:06.820 --> 00:59:08.140
do you're probably not.

00:59:08.500 --> 00:59:11.210
Emotionally ready for homework 2 yet,

00:59:11.210 --> 00:59:12.740
but I'll give it to you anyway.

00:59:14.930 --> 00:59:16.510
Is to show you homework too.

00:59:25.020 --> 00:59:27.760
Alright, so at least in some parts of

00:59:27.760 --> 00:59:30.070
this are going to be a bit familiar.

00:59:32.020 --> 00:59:32.640
Yeah.

00:59:32.640 --> 00:59:33.140
Thank you.

00:59:34.070 --> 00:59:34.750
I always forget.

00:59:35.730 --> 00:59:37.640
With that, let me get rid of that.

00:59:38.500 --> 00:59:39.000
OK.

00:59:42.850 --> 00:59:43.480
Damn it.

00:59:51.800 --> 00:59:55.390
Alright, let's see me in a bit.

00:59:56.330 --> 00:59:56.840
OK.

00:59:57.980 --> 00:59:59.290
All right, so there's three parts of

00:59:59.290 --> 00:59:59.900
this.

00:59:59.900 --> 01:00:04.780
The first part is looking at the

01:00:04.780 --> 01:00:06.920
effects of model complexity with tree

01:00:06.920 --> 01:00:07.610
regressors.

01:00:08.870 --> 01:00:12.560
So you train trees with different

01:00:12.560 --> 01:00:13.190
depths.

01:00:13.800 --> 01:00:17.380
And Oregon, random forests with

01:00:17.380 --> 01:00:18.090
different depths.

01:00:19.120 --> 01:00:22.745
And then you plot the error versus the

01:00:22.745 --> 01:00:24.150
versus the size.

01:00:25.280 --> 01:00:26.440
So it's actually.

01:00:26.440 --> 01:00:27.350
This is actually.

01:00:29.290 --> 01:00:29.980
Pretty easy.

01:00:29.980 --> 01:00:31.720
Code wise, it's, I'll show you.

01:00:31.720 --> 01:00:34.240
It's just to get to just see for

01:00:34.240 --> 01:00:35.890
yourself like the effects of depth.

01:00:37.260 --> 01:00:38.830
So in this case you don't need to

01:00:38.830 --> 01:00:40.590
implement the trees or the random

01:00:40.590 --> 01:00:41.920
forests, you can use the library.

01:00:42.740 --> 01:00:43.940
So, and we're going to use the

01:00:43.940 --> 01:00:44.640
temperature data.

01:00:46.350 --> 01:00:48.910
Essentially you would iterate over

01:00:48.910 --> 01:00:51.360
these Max depths which range from 2 to

01:00:51.360 --> 01:00:52.020
32.

01:00:52.970 --> 01:00:54.890
And then for each depth you would call

01:00:54.890 --> 01:00:58.790
these functions and get the error and

01:00:58.790 --> 01:01:00.300
then you can.

01:01:01.500 --> 01:01:04.570
And then you can call this code to plot

01:01:04.570 --> 01:01:05.030
the error.

01:01:05.670 --> 01:01:07.610
And then you'll look at that plot, and

01:01:07.610 --> 01:01:08.440
then you'll.

01:01:09.250 --> 01:01:11.580
Provide the plot and answer some

01:01:11.580 --> 01:01:12.120
questions.

01:01:12.720 --> 01:01:16.180
So in the report there's some questions

01:01:16.180 --> 01:01:18.090
for you to answer based on your

01:01:18.090 --> 01:01:18.820
analysis.

01:01:20.350 --> 01:01:21.846
They're like, given a maximum depth

01:01:21.846 --> 01:01:26.130
tree, which model has the lowest bias

01:01:26.130 --> 01:01:28.089
for regression trees, what tree depth

01:01:28.090 --> 01:01:29.900
achieves the minimum validation error?

01:01:31.080 --> 01:01:33.440
When is which model is least prone to

01:01:33.440 --> 01:01:34.810
overfitting, for example?

01:01:37.480 --> 01:01:38.970
So that's the first problem.

01:01:40.030 --> 01:01:41.530
The second problem, this is the one

01:01:41.530 --> 01:01:43.485
that's going to take you the most time,

01:01:43.485 --> 01:01:46.950
is using MLPS, so multilayer

01:01:46.950 --> 01:01:48.390
perceptrons with MNIST.

01:01:49.590 --> 01:01:52.770
It takes about 3 minutes to train it,

01:01:52.770 --> 01:01:54.420
so it's not too bad compared to your

01:01:54.420 --> 01:01:55.360
nearest neighbor training.

01:01:56.310 --> 01:01:56.840
And.

01:01:57.680 --> 01:02:01.610
And you need you need to basically

01:02:01.610 --> 01:02:02.680
like.

01:02:02.680 --> 01:02:05.225
We're going to use Pytorch, which is

01:02:05.225 --> 01:02:06.800
like a really good package for deep

01:02:06.800 --> 01:02:07.160
learning.

01:02:08.180 --> 01:02:09.990
And you need to.

01:02:11.750 --> 01:02:15.500
Fill out the forward and.

01:02:16.850 --> 01:02:20.370
And the like model specification.

01:02:20.370 --> 01:02:23.650
So I provide in the chips a link to a

01:02:23.650 --> 01:02:25.500
tutorial and you can also look up other

01:02:25.500 --> 01:02:28.320
tutorials that explain in the tips.

01:02:28.320 --> 01:02:30.510
Also gives you kind of the basic code

01:02:30.510 --> 01:02:30.930
structure.

01:02:31.640 --> 01:02:33.850
But you can see like how these things

01:02:33.850 --> 01:02:36.030
are coded, essentially that you define

01:02:36.030 --> 01:02:37.280
the layers of the network here.

01:02:37.870 --> 01:02:40.560
And then you define like how the data

01:02:40.560 --> 01:02:42.030
progresses through the network to make

01:02:42.030 --> 01:02:45.429
a prediction and then you and then you

01:02:45.430 --> 01:02:46.430
can train your network.

01:02:48.040 --> 01:02:49.410
Obviously we haven't talked about this

01:02:49.410 --> 01:02:50.900
yet, so it might not make complete

01:02:50.900 --> 01:02:52.200
sense yet, but it will.

01:02:53.760 --> 01:02:55.048
So then you're going to train a

01:02:55.048 --> 01:02:57.019
network, then you're going to try

01:02:57.020 --> 01:02:58.638
different learning rates, and then

01:02:58.638 --> 01:03:00.230
you're going to try to get the best

01:03:00.230 --> 01:03:03.340
network you can with the target of 25%

01:03:03.340 --> 01:03:04.000
validation error.

01:03:05.770 --> 01:03:07.150
And then a third problem.

01:03:07.150 --> 01:03:09.450
We're looking at this new data set

01:03:09.450 --> 01:03:11.820
called the Penguin data set, the Palmer

01:03:11.820 --> 01:03:13.500
Archipelago Penguin data set.

01:03:14.410 --> 01:03:16.800
And this is a data set of like some

01:03:16.800 --> 01:03:18.500
various physical measurements of the

01:03:18.500 --> 01:03:19.970
Penguins, whether they're male or

01:03:19.970 --> 01:03:21.813
female, what island they came from, and

01:03:21.813 --> 01:03:23.140
what kind of species it is.

01:03:23.990 --> 01:03:25.800
So we created a clean version of the

01:03:25.800 --> 01:03:28.510
data here and.

01:03:29.670 --> 01:03:31.500
And then we have like some starter code

01:03:31.500 --> 01:03:32.380
to load that data.

01:03:33.210 --> 01:03:35.370
And you're going to 1st like visualize

01:03:35.370 --> 01:03:36.470
some of the features.

01:03:36.470 --> 01:03:40.270
So we did one example for you if you

01:03:40.270 --> 01:03:41.970
look at the different species of

01:03:41.970 --> 01:03:42.740
Penguins.

01:03:44.890 --> 01:03:46.880
This is like a scatter plot of body

01:03:46.880 --> 01:03:48.900
mass versus flipper length for some

01:03:48.900 --> 01:03:49.980
different Penguins.

01:03:49.980 --> 01:03:51.950
So you can see that this would be like

01:03:51.950 --> 01:03:53.880
pretty good at distinguishing Gentoo

01:03:53.880 --> 01:03:57.230
from a deli and chinstrap, but not so

01:03:57.230 --> 01:03:59.030
good at distinguishing chinstrap in a

01:03:59.030 --> 01:03:59.280
deli.

01:03:59.280 --> 01:04:00.790
So you can do this for different

01:04:00.790 --> 01:04:01.792
combinations of features.

01:04:01.792 --> 01:04:03.120
There's not a lot of features.

01:04:03.120 --> 01:04:03.989
I think there's 13.

01:04:06.080 --> 01:04:07.020
And then?

01:04:07.100 --> 01:04:07.730


01:04:08.440 --> 01:04:10.140
And then in the report it asks like

01:04:10.140 --> 01:04:12.410
some kinds of like analysis questions

01:04:12.410 --> 01:04:14.060
based on that feature analysis.

01:04:15.490 --> 01:04:17.410
Then the second question is to come up

01:04:17.410 --> 01:04:19.889
with a simple, really simple rule A2

01:04:19.890 --> 01:04:21.330
part rule that will allow you to

01:04:21.330 --> 01:04:22.980
perfectly classify Gentius.

01:04:24.330 --> 01:04:27.170
And then the third part is to design an

01:04:27.170 --> 01:04:29.385
mill model to maximize your accuracy on

01:04:29.385 --> 01:04:30.160
this problem.

01:04:30.160 --> 01:04:33.070
And you can use you can use like the

01:04:33.070 --> 01:04:35.280
library to do cross validation.

01:04:35.280 --> 01:04:37.610
So essentially you can use the

01:04:37.610 --> 01:04:39.190
libraries for your models as well.

01:04:39.190 --> 01:04:40.390
So you just need to choose the

01:04:40.390 --> 01:04:42.100
parameters of your models and then try

01:04:42.100 --> 01:04:43.569
to get the best performance you can.

01:04:47.330 --> 01:04:49.180
Then the stretch goals are to improve

01:04:49.180 --> 01:04:52.020
the MNIST using MLPS to find a second

01:04:52.020 --> 01:04:54.330
rule for classifying Gentius.

01:04:55.050 --> 01:04:57.660
And then this one is positional

01:04:57.660 --> 01:05:00.765
encoding, which is a way of like

01:05:00.765 --> 01:05:03.130
encoding positions that lets networks

01:05:03.130 --> 01:05:05.170
work better on it, but I won't go into

01:05:05.170 --> 01:05:06.490
details there since we haven't talked

01:05:06.490 --> 01:05:07.070
about networks.

01:05:09.040 --> 01:05:11.270
Any questions about homework 2?

01:05:14.740 --> 01:05:16.100
There will be, yes.

01:05:17.910 --> 01:05:18.190
OK.

01:05:29.410 --> 01:05:29.700
No.

01:05:29.700 --> 01:05:31.484
It says in that you don't need to

01:05:31.484 --> 01:05:31.893
answer them.

01:05:31.893 --> 01:05:34.470
You don't need to report on them.

01:05:34.470 --> 01:05:36.450
So you should answer them in your head

01:05:36.450 --> 01:05:37.936
and you'll learn more that way, but you

01:05:37.936 --> 01:05:39.220
don't need to provide the answer.

01:05:40.190 --> 01:05:40.710
Yeah.

01:05:43.900 --> 01:05:44.230
Why?

01:05:47.670 --> 01:05:48.830
Will not make a cost.

01:05:51.690 --> 01:05:53.280
No, it won't hurt you either.

01:05:54.650 --> 01:05:54.910
Yeah.

01:05:55.930 --> 01:05:56.740
You're not required.

01:05:56.740 --> 01:05:58.397
You're only required to fill out what's

01:05:58.397 --> 01:05:59.172
in the template.

01:05:59.172 --> 01:06:01.880
So sometimes I say to do like slightly

01:06:01.880 --> 01:06:03.406
more than what's in the template.

01:06:03.406 --> 01:06:05.300
The template is basically to show that

01:06:05.300 --> 01:06:07.226
you've done it, so sometimes you can

01:06:07.226 --> 01:06:08.520
show that you've done it without

01:06:08.520 --> 01:06:09.840
providing all the details.

01:06:09.840 --> 01:06:10.220
So.

01:06:16.180 --> 01:06:17.810
So the question is, can you resubmit

01:06:17.810 --> 01:06:18.570
the assignment?

01:06:18.570 --> 01:06:20.363
I wouldn't really recommend it.

01:06:20.363 --> 01:06:21.176
You would get.

01:06:21.176 --> 01:06:23.570
So the way that it works is that at the

01:06:23.570 --> 01:06:25.653
time that the T at the, it's mainly T

01:06:25.653 --> 01:06:27.459
is greeting, so at the time that the

01:06:27.460 --> 01:06:28.250
tea is green.

01:06:29.270 --> 01:06:31.060
Whatever is submitted last will be

01:06:31.060 --> 01:06:31.480
graded.

01:06:32.390 --> 01:06:34.930
And whatever, like with whatever late

01:06:34.930 --> 01:06:36.950
days have accrued for that, for that

01:06:36.950 --> 01:06:37.360
submission.

01:06:37.360 --> 01:06:40.140
If it's late so you can resubmit, but

01:06:40.140 --> 01:06:41.590
then once they've graded, then it's

01:06:41.590 --> 01:06:43.270
graded and then you can't resubmit

01:06:43.270 --> 01:06:43.640
anymore.

01:06:46.300 --> 01:06:47.150
There were.

01:06:47.150 --> 01:06:48.910
We basically assume that if it's past

01:06:48.910 --> 01:06:50.530
the deadline and you've submitted, then

01:06:50.530 --> 01:06:54.580
we can grade it and so it might get and

01:06:54.580 --> 01:06:56.750
generally if you want to get extra

01:06:56.750 --> 01:06:57.170
points.

01:06:57.900 --> 01:06:59.330
I would just recommend a move on to

01:06:59.330 --> 01:07:01.053
homework two and do extra points for

01:07:01.053 --> 01:07:02.430
homework two rather than getting stuck

01:07:02.430 --> 01:07:03.925
on homework one and getting late days

01:07:03.925 --> 01:07:06.040
and then like having trouble getting up

01:07:06.040 --> 01:07:07.250
getting homework 2 done.

01:07:13.630 --> 01:07:16.730
All right, so the things to remember

01:07:16.730 --> 01:07:17.420
from this class.

01:07:18.180 --> 01:07:20.180
Ensembles improve accuracy and

01:07:20.180 --> 01:07:22.325
confidence estimates by reducing the

01:07:22.325 --> 01:07:23.990
bias and Oregon the variance.

01:07:23.990 --> 01:07:25.730
And there's like this really important

01:07:25.730 --> 01:07:28.100
principle that test error can be

01:07:28.100 --> 01:07:30.690
decomposed into variance, bias and

01:07:30.690 --> 01:07:31.670
irreducible noise.

01:07:32.680 --> 01:07:33.970
And because the trees and random

01:07:33.970 --> 01:07:35.870
forests are really powerful and widely

01:07:35.870 --> 01:07:38.000
applicable classifiers and regressors.

01:07:39.990 --> 01:07:43.440
So in the next class I'm going to talk

01:07:43.440 --> 01:07:45.765
about SVM support vector machines,

01:07:45.765 --> 01:07:48.910
which were very popular approach, and

01:07:48.910 --> 01:07:50.830
stochastic gradient descent, which is a

01:07:50.830 --> 01:07:52.310
method to optimize them that also

01:07:52.310 --> 01:07:54.245
applies to neural Nets and deep Nets.

01:07:54.245 --> 01:07:56.300
So thank you, I'll see you on Thursday.

01:19:53.620 --> 01:19:54.020
Yeah.

01:19:56.250 --> 01:19:56.660
Testing.

01:19:58.350 --> 01:19:58.590
Yeah.